Catholic High School Level 3 Physics 2025 Notes (PDF)

Catholic High School Level 3 Physics: 2025 Notes (02) Kinematics A. Content Speed, Velocity and Acceleration Graphical...

Catholic High School Level 3 Physics: 2025 Notes (02) Kinematics A. Content Speed, Velocity and Acceleration Graphical Analysis of Motion Acceleration of Free-Fall B. Learning Outcomes Students should be able to: (a) state what is meant by speed and velocity (b) calculate average speed = distance travelled / time taken (c) state what is meant by uniform acceleration and calculate the value of an acceleration using change in velocity / time taken (d) interpret given examples of non-uniform acceleration (e) plot and interpret a displacement-time graph and a velocity-time graph for motion in one dimension (f) deduce from the shape of a displacement-time graph when a body is: (i) at rest (ii) moving with uniform velocity (iii) moving with non-uniform velocity (g) deduce from the shape of a velocity-time graph when a body is: (i) at rest (ii) moving with uniform velocity (iii) moving with uniform acceleration (iv) moving with non-uniform acceleration (h) calculate the area under a velocity-time graph to determine the displacement travelled for motion with uniform velocity or uniform acceleration (i) state that the acceleration of free fall for a body near to the Earth is constant and is approximately 10 m / s2 Re-visit Chapter 1: (e) select and explain the use of appropriate measuring instruments to measure or determine physical quantities taking into consideration the range and precision of the instrument C. References 1. Chew C., Ho B.T., Low B.Y., Yeow K.H. (2023). GCE ‘O’ Level: Physics Matters (5th ed). Marshall Cavendish Education. D. Notes Outline 1. Scalars and Vectors 2. Distance and Displacement 3. Speed and Velocity 4. Calculating Speed using Ticker-Tape Timer 5. Acceleration 6. Graphs of Motion 7. Acceleration of Free Fall 8. Appendix: Equations of Motion (Optional) Page 1 of 17 1. SCALARS AND VECTORS Scalar quantity: Physical quantity having magnitude only. E.g.: time, length, speed, mass, volume, density, energy, work done, power, current, resistance. Vector quantity: Physical quantity having both magnitude and direction. Direction of vector: stated using 25 angle with respect to the horizontal or vertical (e.g. 25 to the horizontal) left / right, vertically upwards / downwards (in such cases, where motion is along one linear dimension, a sign convention can be chosen where “+” and “-” signs are used to denote direction) North, Southeast, etc. (ONLY for cases where the compass points are already stated in the question) E.g.: displacement, velocity, acceleration force (e.g. weight, tension) moment of a force (direction is clockwise or anti-clockwise) Note: The above 5 examples are the only vector quantities to be taught in this syllabus. Page 2 of 17 2. DISTANCE AND DISPLACEMENT Distance, s: (scalar quantity) Total length covered by a moving object regardless of the direction of motion. SI unit: metre, m Displacement, s: (vector quantity) Distance measured in a straight line in a specified direction. SI unit: metre, m Example End point 8m Start point 25 20 m Distance travelled by the object is represented by the length of the dotted line. Displacement of the object is represented by the length of the arrow. In the figure above: Distance travelled = 20 m. Displacement = 8 m, at an angle of 25 to the horizontal. Example Consider the following: Motion 1: A student walked 3 m to the left. State the distance he has covered. State his displacement from his starting position. Motion 2: The student then walked another 4 m to the right. State the total distance he has covered. State his displacement from his starting position. Page 3 of 17 Example A student bounces a ball on the ground and the ball rises to a point higher than the original position and returns to his hand as shown in the diagram. 0.5 m (Sign convention) Taking upwards as positive: The total distance travelled by the ball is 2.0 m. (True / False) 1.5 m The total displacement of the ball is +0.5 m. (True / False) The displacement of the ball at the highest point is +0.5 m. (True / False) The displacement of the ball at the lowest point is -1.5 m. (True / False) Example A car travels 3 km due east from point O to A and then a further 3 km due north of A to B. Determine the distance covered and its displacement. N B O A 3. SPEED AND VELOCITY (a) state what is meant by speed and velocity (b) calculate average speed = distance travelled / time taken Speed, v: Velocity, v: (scalar quantity) (vector quantity) Rate of change of distance. Rate of change of displacement. or or Change of distance per unit time. Change of displacement per unit time. 𝒔 𝒔 v= (for constant v only) v= (for constant v only) 𝒕 𝒕 Note: ‘rate’ = ‘per unit time’ SI unit: metre per second, m s-1 SI unit: metre per second, m s-1 Average speed (or velocity), v: Total distance (or displacement) divided by total time taken. Total s Average v = Total t Page 4 of 17 Instantaneous speed (or velocity), v: Speed (or velocity) at a particular instant. 𝑑𝑠 (For information only: v =.) 𝑑𝑡 Note: ds and dt means a very small (i.e. infinitesimally small) change in distance/displacement and time respectively, which will be taught in ‘Differentiation’ during L4 Mathematics lessons. The instantaneous speed (or instantaneous velocity) is usually found graphically by finding the gradient of a distance-time (or displacement-time) graph at a particular instant. Example A toy car travels at 3.0 m s-1 for 50 m and then stops for 2.0 min. It then travels at 7.5 m s-1 for 10 m. Find the average speed of the car. Example State whether an MRT train can have an instantaneous speed of 30 m s-1 and an average speed of 10 m s-1. Explain your answer. Example Convert a) 10 m s-1 to km h-1 b) 80 km h-1 to m s-1 Page 5 of 17 4. CALCULATING SPEED USING TICKER-TAPE TIMER (From Chapter 1) (a) select and explain the use of appropriate measuring instruments to measure or determine physical quantities taking into consideration the range and precision of the instrument A ticker-tape timer is a device that can be used to determine the speed of an object. A long paper tape is attached to a moving object and threaded through a device that places a dot upon the tape at regular intervals of time. As the object moves, it drags the tape through the ‘ticker’, thus leaving a trail of dots. The trail of dots provides a history of the object's motion and therefore a representation of the object's motion. → Watch a video of a ticker-tape timer: https://tinyurl.com/CHS-tickertape To find speed using a ticker-tape timer, we need to first be able to determine the distance travelled by the object by measuring the length of the path taken. In this case, the distance travelled is 12.0 cm. For time taken, we will need to count the number of intervals made by the dots. In this case, there are 10 intervals. To know the time taken for each interval, you will need to look at the frequency of the ticker-tape timer. It is usually determined by the number of dots produced per second. For example, if a ticker tape timer makes 50 dots every second (ie. frequency of 50 Hz), the time taken for each interval 1 1 is s. Since we have 10 intervals, the time taken is 10 × = 0.20 s. 50 50 Speed = Distance ÷ Time = 12.0 ÷ 0.20 s = 60.0 cm s-1 (3 s.f.) In general, the closer the dots are, the slower the ticker-tape is being pulled; conversely, the further the dots are, the faster the ticker-tape is being pulled. Page 6 of 17 Example The diagram shows a strip of paper tape that has been pulled under a vibrating arm by an object travelling at a steady speed. The arm is vibrating regularly, making 40 dots per second. Determine the speed of the object. Example A moving car has oil dripping at a constant rate. The pattern of drips on the road is shown in the diagram below. Which is the correct description of the motion of the car? A It travelled at a steady speed and then accelerated. B It travelled at a steady speed and then slowed down. C It accelerated and then slowed down. D It accelerated and then travelled at a steady speed. Page 7 of 17 5. ACCELERATION (c) state what is meant by uniform acceleration and calculate the value of an acceleration using change in velocity / time taken (include the use of ticker-tape timer) (d) interpret given examples of non-uniform acceleration Acceleration, a: (vector quantity) Rate of change of velocity or Change of velocity per unit time change in velocity ∆𝒗 𝒗−𝒖 a= = = total time ∆𝒕 𝒕 where:  represents ‘change in’, v = final velocity, m s-1, u = initial velocity, m s-1 SI unit: metre per squared second, m s-2 There is acceleration when there is (a) a change in speed, (b) a change in direction, or (c) a change in both speed and direction. Example A toy car travels at 3.0 m s-1 for 50 m and comes to a stop in 10 s. Calculate the acceleration of the car. Example Evaluate the following statements about acceleration: a. When an object accelerates, its velocity always increases. (True / False) b. When an object accelerates, its speed may remain constant. (True / False) Example 1. When the velocity of an object is zero, can its acceleration be non-zero? Why? 2. When the velocity of an object is non-zero, can its acceleration be zero? Why? 3. When the velocity of an object is positive, can its acceleration be negative? Why? Page 8 of 17 6. GRAPHS OF MOTION (e) plot and interpret a displacement-time graph and a velocity-time graph (f) deduce from the shape of a displacement-time graph when a body is: (i) at rest (ii) moving with uniform velocity (iii) moving with non-uniform velocity (g) deduce from the shape of a velocity-time graph when a body is: (i) at rest (ii) moving with uniform velocity (iii) moving with uniform acceleration (iv) moving with non-uniform acceleration (h) calculate the area under a velocity-time graph to determine the displacement travelled for motion with uniform velocity or uniform acceleration 6.1. DISPLACEMENT-TIME GRAPHS The figure shows a car travelling along a straight line in one direction, away from the starting point O. If the direction to the right is set as positive, then the positive gradients of graphs in (b) to (d) mean that the car is travelling towards the right. The displacement of the car is measured for every second. The displacements and times are recorded and a graph is plotted using the data. The results for four possible journeys are shown below. Page 9 of 17 6.2. VELOCITY-TIME GRAPHS A boy playing in a video arcade controls his car by stepping on a pedal. Velocity-time graphs can be used to illustrate uniform and non-uniform acceleration of his motion in one direction in a straight line. Page 10 of 17  Displacement-Time Graph Velocity-Time Graph Acceleration-Time Graph s v a gradient gradient =m =m 0 t t t 0 0 Gradient Gradient Gradient: no significance Change in displacement Change in velocity = = Change in time Change in time = velocity = acceleration Area under the graph: Area under the graph Area under the graph no significance = change in displacement = change in velocity (this is not required for the O-Level syllabus) Example The velocity-time graph of a car is shown below. Describe the motion of the car. velocity acceleration 0 – 5 s: 5 – 10 s: 10 – 15 s: 15 – 20 s: 20 – 25 s: 25 – 30 s: 30 – 35 s: Page 11 of 17 6.3. ANALYSIS OF GRAPHS OF MOTION (VELOCITY-TIME GRAPHS) Analysis 1 v v v 0 0 0 t t t Velocity Positive Positive Negative (+ or -) Speed Constant Increasing Increasing ( or ) Gradient Zero Positive Negative (+ or -) Change in No change No change No change gradient (gradient = 0) (gradient is constant) (gradient is constant) ( or ) Moving with increasing Moving with increasing Describing Moving at a constant speed speed speed the motion (in the positive direction) (in the positive direction) (in the negative direction) Page 12 of 17 Analysis 2 v v 0 0 t t Velocity Zero to positive Positive (+ or -) Speed Increasing Increasing ( or ) Gradient Zero to positive Positive (+ or -) Change in gradient Increasing Decreasing ( or ) Moving from rest with speed Moving from rest with speed Describing the increasing at an increasing rate increasing at a decreasing rate motion (in the positive direction) (in the positive direction) Example The graph below shows the velocity-time graph of a moving car. The velocity of the car increases uniformly along OA, then becomes constant over the section AB and finally decreases uniformly A B along BC until the car comes to rest at C. (a) Determine the acceleration of the car for the first 4 s. (b) State the acceleration of the car between 4 s and 18 s. Show your workings or explain your answer clearly. C (c) Determine the acceleration of the car for the last 2 s. O (d) Determine the total distance travelled by the car in 20 s. Page 13 of 17 7. ACCELERATION OF FREE FALL (i) state that the acceleration of free fall for a body near to the Earth is constant and is approximately 10 m / s2 The force of gravity pulls down all objects here on the Earth, giving rise to our weight. When an object is said to be in free fall, the only force acting on it is its weight or the gravitational force. (ie. there is no air resistance.) All free-falling objects near the surface of the Earth, regardless of mass and size, will experience a constant acceleration when it is allowed to fall freely under the Earth’s gravitational pull. This acceleration due to gravity is denoted by g. It is usually approximated to 10 m s-2. In the absence of air resistance, objects that are released from rest from the same height will reach the ground at the same time regardless of mass and size. In reality, an object falling through air will always experience air resistance. You will learn more about the motion of objects falling through air (including the forces acting on them, as well as the corresponding displacement-time and velocity-time graphs) in Chapter 3: Dynamics. Page 14 of 17 APPENDIX 8. EQUATIONS OF MOTION (OPTIONAL) Objective: To solve problems using the following equations which represent uniformly accelerated motion in a straight line, including the motion of bodies free-falling in a uniform gravitational field (ie. without air resistance): 𝑣−𝑢 a= , s = ½(u + v)t, v2 = u2 + 2as, s = ut + ½ at2 𝑡 Consider a body moving in a straight line with uniform acceleration a. v / m s-1 v Assume the initial velocity u of the body increases uniformly to a final velocity v during a total time t. From the definition of acceleration: u change in velocity a= = gradient of v-t graph time 𝑣−𝑢 a= --- (1) 𝑡 t/s t s = displacement travelled = area under v-t graph s = ½(u + v)t --- (2) Substitute (1) (in the form v = u + at) into (2): s = ut + ½at2 --- (3) Squaring (1) (in the form t = (v - u)/a) and substitute into (2): v2 = u2 + 2as --- (4) Note: The proofs above are for information only. Therefore the 4 equations of motion are: 𝒗–𝒖 a= 𝒕 s = ½(u + v)t s = ut + ½at2 v2 = u2 + 2as Example A girl throws a ball vertically upwards with a speed of 10 m s-1. What is the acceleration of the ball one second after leaving the girl’s hand? (A) 0 m s-2 (B) 5 m s-2 downwards (C) 10 m s-2 downwards (D) 10 m s-2 upwards Page 15 of 17 Example An object is released from rest and allowed to reach the ground. If the same object is released from the same height above the surfaces of different planets, state and explain whether the time taken for the object to reach the ground will differ. Example A man throws a stone vertically up to another man standing at a height of 2.0 m above. If the stone is thrown up with a velocity of 7.0 m s-1, what is the velocity of the stone at the instant when it is caught by the man? s u v a t Example A spacecraft is travelling with a velocity of 3250 m s-1. Suddenly the retrorocket is fired, and the spacecraft begins to slow down with an acceleration of magnitude 10.0 m s-2. Calculate the velocity of the spacecraft when its displacement is 215 km, relative to the point where the retrorocket began firing. s u v a t Page 16 of 17 Example A stone is thrown upwards with a speed of 12 m s-1 from the edge of a cliff 100 m high. Determine (a) the time taken for the stone to reach the bottom of the cliff, (b) the speed just before hitting the bottom of the cliff, (c) the total distance it traveled. Sketch a graph showing how the velocity of the stone varies with time and label the axes with the appropriate values (take t = 0 s to be the time that the stone is thrown.) Page 17 of 17