Edexcel Maths M1 Past Paper Questions (January 2005) PDF

Page 1 from 88 Edexcel Maths M1 Topic Questions from Papers Kinematics  January 2005 Leave...

Page 1 from 88 Edexcel Maths M1 Topic Questions from Papers Kinematics  January 2005 Leave blank 3. Figure 2 speed (m s–1) 9 u O 4 20 25 time (s) A sprinter runs a race of 200 m. Her total time for running the race is 25 s. Figure 2 is a sketch of the speed-time graph for the motion of the sprinter. She starts from rest and accelerates uniformly to a speed of 9 m s–1 in 4 s. The speed of 9 m s–1 is maintained for 16 s and she then decelerates uniformly to a speed of u m s–1 at the end of the race. Calculate (a) the distance covered by the sprinter in the first 20 s of the race, (2) (b) the value of u, (4) (c) the deceleration of the sprinter in the last 5 s of the race. (3) __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ N16740A 6  January 2005 Leave blank Question 3 continued __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ Q3 (Total 9 marks) N16740A 7 Turn over  EDEXCEL M1 IAL OCTOBER 2017 Leave blank 6. An athlete goes for a run along a straight horizontal road. Starting from rest, she accelerates at 0.6 m s–2 up to a speed of V m s–1. She then maintains this constant speed of V m s–1 before finally decelerating at 0.2 m s–2 back to rest. She covers a total distance DO NOT WRITE IN THIS AREA of 1500 m in 270 s. (a) Sketch a speed-time graph to represent the athlete’s run. (2) 5V (b) Show that she accelerates for seconds. 3 (2) (c) Show that V 2 – kV + 450 = 0, where k is a constant to be found. (6) (d) Find the value of V, justifying your answer. (4) ___________________________________________________________________________ ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 20 *P50804A02028*  EDEXCEL M1 IAL OCTOBER 2017 Leave blank Question 6 continued ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 21 *P50804A02128* Turn over  EDEXCEL M1 IAL JUNE 2017 Leave blank 5. Two trains, P and Q, move on horizontal parallel straight tracks. Initially both are at rest in a station and level with each other. At time t = 0, P starts off and moves with constant acceleration for 10 s up to a speed of 25 m sí1 and then moves at a constant speed of 25 m sí1. At time t = 20, where t is measured in seconds, train Q starts to move in the same direction as P. Train Q accelerates with the same initial constant acceleration as P, up to a speed of 40 m sí1 and then moves at a constant speed of 40 m sí1. Train Q overtakes P at time t = T, after both trains have reached their constant speeds. (a) Sketch, on the same axes, the speed-time graphs of both trains for 0 - t - T. (3) (b) Find the value of t at the instant when both trains are moving at the same speed. (2) (c) Find the value of T. (8) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 16 *P50714A01628*  EDEXCEL M1 IAL JUNE 2017 Leave blank Question 5 continued ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ DO NOT WRITE IN THIS AREA ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 17 *P50714A01728* Turn over  June 2005 Leave blank 1. In taking off, an aircraft moves on a straight runway AB of length 1.2 km. The aircraft moves from A with initial speed 2 m s–1. It moves with constant acceleration and 20 s later it leaves the runway at C with speed 74 m s–1. Find (a) the acceleration of the aircraft, (2) (b) the distance BC. (4) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ *N20911A0220* 2  June 2005 Leave blank 5. A train is travelling at 10 m s–1 on a straight horizontal track. The driver sees a red signal 135 m ahead and immediately applies the brakes. The train immediately decelerates with constant deceleration for 12 s, reducing its speed to 3 m s–1. The driver then releases the brakes and allows the train to travel at a constant speed of 3 m s–1 for a further 15 s. He then applies the brakes again and the train slows down with constant deceleration, coming to rest as it reaches the signal. (a) Sketch a speed-time graph to show the motion of the train, (3) (b) Find the distance travelled by the train from the moment when the brakes are first applied to the moment when its speed first reaches 3 m s–1. (2) (c) Find the total time from the moment when the brakes are first applied to the moment when the train comes to rest. (5) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ *N20911A01020* 10  June 2005 Leave blank Question 5 continued ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ Q5 (Total 10 marks) *N20911A01120* 11 Turn over  January 2006 Leave blank 1. A stone is thrown vertically upwards with speed 16 m s–1 from a point h metres above the ground. The stone hits the ground 4 s later. Find (a) the value of h, (3) (b) the speed of the stone as it hits the ground. (3) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ *N20875A0220* 2  June 2006 Leave blank 1. Figure 1 v (m s–1) 5 2 O 3 7 t (s) Figure 1 shows the speed-time graph of a cyclist moving on a straight road over a 7 s period. The sections of the graph from t = 0 to t = 3, and from t = 3 to t = 7, are straight lines. The section from t = 3 to t = 7 is parallel to the t-axis. State what can be deduced about the motion of the cyclist from the fact that (a) the graph from t = 0 to t = 3 is a straight line, (1) (b) the graph from t = 3 to t = 7 is parallel to the t-axis. (1) (c) Find the distance travelled by the cyclist during this 7 s period. (4) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ *N22331A0216* 2  June 2006 Leave blank 3. A train moves along a straight track with constant acceleration. Three telegraph poles are set at equal intervals beside the track at points A, B and C, where AB = 50 m and BC = 50 m. The front of the train passes A with speed 22.5 m s–1, and 2 s later it passes B. Find (a) the acceleration of the train, (3) (b) the speed of the front of the train when it passes C, (3) (c) the time that elapses from the instant the front of the train passes B to the instant it passes C. (4) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ *N22331A0616* 6  January 2007 Leave blank 5. A ball is projected vertically upwards with speed 21 m s–1 from a point A, which is 1.5 m above the ground. After projection, the ball moves freely under gravity until it reaches the ground. Modelling the ball as a particle, find (a) the greatest height above A reached by the ball, (3) (b) the speed of the ball as it reaches the ground, (3) (c) the time between the instant when the ball is projected from A and the instant when the ball reaches the ground. (4) ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ *N23560A01016* 10  January 2007 Leave blank Question 5 continued ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________ Q5 (Total 10 marks) *N23560A01116* 11 Turn over  June 2007 Leave blank 4. A car is moving along a straight horizontal road. At time t = 0, the car passes a point A with speed 25 m s–1. The car moves with constant speed 25 m s–1 until t = 10 s. The car then decelerates uniformly for 8 s. At time t = 18 s, the speed of the car is V m s–1 and this speed is maintained until the car reaches the point B at time t = 30 s. (a) Sketch, in the space below, a speed–time graph to show the motion of the car from A to B. (3) Given that AB = 526 m, find (b) the value of V, (5) (c) the deceleration of the car between t = 10 s and t = 18 s. (3) _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ 8 *N26114A0820*  June 2007 Leave blank Question 4 continued _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________ 9 *N26114A0920* Turn over  January 2008 Leave blank 2. A firework rocket starts from rest at ground level and moves vertically. In the first 3 s of its motion, the rocket rises 27 m. The rocket is modelled as a particle moving with constant acceleration a m s–2. Find (a) the value of a, (2) (b) the speed of the rocket 3 s after it has left the ground. (2) After 3 s, the rocket burns out. The motion of the rocket is now modelled as that of a particle moving freely under gravity. (c) Find the height of the rocket above the ground 5 s after it has left the ground. (4) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 4 *M26331A0428*  January 2008 Leave blank 3. A car moves along a horizontal straight road, passing two points A and B. At A the speed of the car is 15 m s–1. When the driver passes A, he sees a warning sign W ahead of him, 120 m away. He immediately applies the brakes and the car decelerates with uniform deceleration, reaching W with speed 5 m s–1. At W, the driver sees that the road is clear. He then immediately accelerates the car with uniform acceleration for 16 s to reach a speed of V m s–1 (V > 15). He then maintains the car at a constant speed of V m s–1. Moving at this constant speed, the car passes B after a further 22 s. (a) Sketch, in the space below, a speed-time graph to illustrate the motion of the car as it moves from A to B. (3) (b) Find the time taken for the car to move from A to B. (3) The distance from A to B is 1 km. (c) Find the value of V. (5) 6 *M26331A0628*  January 2008 Leave blank Question 3 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 7 *M26331A0728* Turn over  June 2008 Leave blank 2. At time t = 0, a particle is projected vertically upwards with speed u m s–1 from a point 10 m above the ground. At time T seconds, the particle hits the ground with speed 17.5 m s–1. Find (a) the value of u, (3) (b) the value of T. (4) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 4 *H29492A0424*  June 2008 Leave blank 4. A car is moving along a straight horizontal road. The speed of the car as it passes the point A is 25 m s–1 and the car maintains this speed for 30 s. The car then decelerates uniformly to a speed of 10 m s–1. The speed of 10 m s–1 is then maintained until the car passes the point B. The time taken to travel from A to B is 90 s and AB = 1410 m. (a) Sketch, in the space below, a speed-time graph to show the motion of the car from A to B. (2) (b) Calculate the deceleration of the car as it decelerates from 25 m s–1 to 10 m s–1. (7) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 8 *H29492A0824*  June 2008 Leave blank Question 4 continued ________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Q4 (Total 9 marks) 9 *H29492A0924* Turn over  January 2009 Leave blank 2. A small ball is projected vertically upwards from ground level with speed u m s–1. The ball takes 4 s to return to ground level. (a) Draw, in the space below, a velocity-time graph to represent the motion of the ball during the first 4 s. (2) (b) The maximum height of the ball above the ground during the first 4 s is 19.6 m. Find the value of u. (3) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 4 *N29411A0424*  June 2009 Leave blank 1. Three posts P, Q and R, are fixed in that order at the side of a straight horizontal road. The distance from P to Q is 45 m and the distance from Q to R is 120 m. A car is moving along the road with constant acceleration a m s–2. The speed of the car, as it passes P, is u m s–1. The car passes Q two seconds after passing P, and the car passes R four seconds after passing Q. Find (i) the value of u, (ii) the value of a. (7) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 2 *N34275A0224*  January 2010 Leave blank 2. An athlete runs along a straight road. She starts from rest and moves with constant acceleration for 5 seconds, reaching a speed of 8 m s–1. This speed is then maintained for T seconds. She then decelerates at a constant rate until she stops. She has run a total of 500 m in 75 s. (a) In the space below, sketch a speed-time graph to illustrate the motion of the athlete. (3) (b) Calculate the value of T. (5) 4 *M35104A0424*  June 2010 Leave blank 5. Two cars P and Q are moving in the same direction along the same straight horizontal road. Car P is moving with constant speed 25 m s −1. At time t = 0, P overtakes Q which is moving with constant speed 20 m s −1. From t = T seconds, P decelerates uniformly, coming to rest at a point X which is 800 m from the point where P overtook Q. From t = 25 s, Q decelerates uniformly, coming to rest at the same point X at the same instant as P. (a) Sketch, on the same axes, the speed-time graphs of the two cars for the period from t = 0 to the time when they both come to rest at the point X. (4) (b) Find the value of T. (8) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 12 *N35390A01228*  June 2010 Leave blank Question 5 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 13 *N35390A01328* Turn over  June 2010 Leave blank 6. A ball is projected vertically upwards with a speed of 14.7 m s −1 from a point which is 49 m above horizontal ground. Modelling the ball as a particle moving freely under gravity, find (a) the greatest height, above the ground, reached by the ball, (4) (b) the speed with which the ball first strikes the ground, (3) (c) the total time from when the ball is projected to when it first strikes the ground. (3) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 16 *N35390A01628*  June 2010 Leave blank Question 6 continued ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ________________________________________