EDEXCEL M1 January 2005 Past Paper PDF

EDEXCEL M1 January 2005 Leave blank 3. Figure 2...

EDEXCEL M1 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) __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ EDEXCEL M1 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 EDEXCEL M1 January 2013 Leave blank 5. v (m s −1 ) 30 O t (s) T Figure 4 The velocity-time graph in Figure 4 represents the journey of a train P travelling along a straight horizontal track between two stations which are 1.5 km apart. The train P leaves the first station, accelerating uniformly from rest for 300 m until it reaches a speed of 30 m s–1. The train then maintains this speed for T seconds before decelerating uniformly at 1.25 m s–2, coming to rest at the next station. (a) Find the acceleration of P during the first 300 m of its journey. (2) (b) Find the value of T. (5) A second train Q completes the same journey in the same total time. The train leaves the first station, accelerating uniformly from rest until it reaches a speed of V m s–1 and then immediately decelerates uniformly until it comes to rest at the next station. (c) Sketch on the diagram above, a velocity-time graph which represents the journey of train Q. (2) (d) Find the value of V. (6) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 16 *P41481A01628* WME01 OCT 2020 Leave blank 8. Acceleration (m s−2) 3 1.5 O 4 24 26 Time (t seconds) −4 Figure 5 The acceleration-time graph shown in Figure 5 represents part of a journey made by a car along a straight horizontal road. The car accelerated from rest at time t = 0 (a) Find the distance travelled by the car during the first 4 s of its journey. (2) (b) Find the total distance travelled by the car during the first 26 s of its journey. (6) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 28 *P65760A02832* WME01 OCT 2021 Leave blank 6. v m s–1 O 2.5 7 t seconds Figure 3 A small ball is thrown vertically upwards at time t = 0 from a point A which is above horizontal ground. The ball hits the ground 7 s later. The ball is modelled as a particle moving freely under gravity. The velocity‑time graph shown in Figure 3 represents the motion of the ball for 0  t  7 (a) Find the speed with which the ball is thrown. (2) (b) Find the height of A above the ground. (3) ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 22 *P66649A02232*  WME01 JAN 2023 1. A train travels along a straight horizontal track between two stations A and B. The train starts from rest at station A and accelerates uniformly for T seconds until it DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA reaches a speed of 20 m s−1 The train then travels at a constant speed of 20 m s−1 for 3 minutes before decelerating uniformly until it comes to rest at station B. The magnitude of the acceleration of the train is twice the magnitude of the deceleration. (a) On the axes below, sketch a speed–time graph to illustrate the motion of the train as it moves from station A to station B. speed (m s−1) O time (s) If you need to redraw your graph, use the axes on page 3 (3) Stations A and B are 4.8 km apart. (b) Find the value of T (5) (c) Find the acceleration of the train during the first T seconds of its motion. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 2 *P72070A0228*   WME01 JAN 2023 Question 1 continued _____________________________________________________________________________________ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Only use these axes if you need to redraw your graph. speed (m s−1) O time (s) (Total for Question 1 is 10 marks) 3  *P72070A0328* Turn over WME01 MAY 2023 5. speed (m s–1) DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA V time (s) 0 30 T Figure 2 The speed-time graph in Figure 2 illustrates the motion of a car travelling along a straight horizontal road. At time t = 0 , the car starts from rest and accelerates uniformly for 30 s until it reaches a speed of V m s–1 The car then travels at a constant speed of V m s–1 until time t = T seconds. (a) Show that the distance travelled by the car between t = 0 and t = T seconds is V (T – 15) metres. (2) A motorbike also travels along the same road. The motorbike starts from rest at time t = 10 s and accelerates uniformly for 40 s The acceleration of the motorbike is the same as the acceleration of the car The motorbike then travels at a constant speed for a further 10 s before decelerating uniformly until it reaches a speed of V m s–1 at time T seconds (b) On Figure 2, sketch a speed-time graph for the motion of the motorbike. [If you need to redraw your sketch, there is a copy of Figure 2 on page 15.] (2) 4V (c) Show that the constant speed of the motorbike is m s–1 3 (2) At time t = T seconds, the distance travelled by each vehicle is the same. (d) Find the value of T (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 12 *P72902A01228*   WME01 MAY 2023 Question 5 continued _____________________________________________________________________________________ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 13  *P72902A01328* Turn over WME01 OCT 2023 2. acceleration DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA (m s–2) 1.2 O time (s) 4 10 20 – 0.5 Figure 2 Two fixed points, A and B, are on a straight horizontal road. The acceleration-time graph in Figure 2 represents the motion of a car travelling along the road as it moves from A to B. At time t = 0, the car passes through A with speed 8 m s–1 At time t = 20 s, the car passes through B with speed v m s–1 (a) Show that v = 18 (3) (b) Sketch a speed-time graph for the motion of the car from A to B. (3) (c) Find the distance AB. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 *P74321A0428*   WME01 OCT 2023 Question 2 continued _____________________________________________________________________________________ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 5  *P74321A0528* Turn over WME01 JAN 2024 6. A particle is projected vertically upwards from a point A with speed 24 m s–1 The point A is 2.5 m vertically above the point B. Point B lies on horizontal ground. The particle moves freely under gravity until it hits the ground at B with speed V m s–1 After hitting the ground the particle does not rebound. (a) Find the value of V. (3) (b) Find the time taken for the particle to reach B. (3) The point C is 10 m vertically above A. (c) Find the length of time for which the particle is above C. (4) (d) Sketch a speed-time graph for the motion of the particle from projection to the instant that it reaches B. (No further calculations are required.) (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 16 *P74317A01628*  WME01 EXAM STYLE QUESTION –1 1. A particle is projected vertically upwards from a point A with speed 29.4 ms The point A is H meters vertically above the point B. Point B lies on horizontal ground. The particle moves freely under gravity until it hits the ground at B with speed V m s–1 After hitting the ground the particle does not rebound. (a) Find the value of u. (1) (b) i) Explain why the particle reaches the greatest height at t = T1 (1) ii) Find the value of T1. (1) iii) Find the greatest height reached above the point of projection (1) The point A is 34.3 m vertically above B. (c) Find the length of time from the greatest height till it hits the ground at B. (4) 16 *P74317A01628* 