NJC Motion and Forces Problem Set 2025

National Junior College Science Department | Physics 3. Motion and Forces Problem Set 3.1 KINEMATICS 3.1.1 Exercises For this section of the problem set, you should try the exercises without looking at the solutions. The solutions are there if you get stuck and you should also use it to understand how to present your work. E1 Distinguish whether the following statements describe speed, velocity, distance, or displacement. (a) The ship sailed south-west for 200 km. (b) I averaged 11 km h−1 during the marathon. (c) The snail crawled at 2 mm s−1 along the straight edge of a bench. (d) The sales representative’s round trip was 420 km. E2 Explain whether the speedometer of a car registers its speed or velocity. E3 A student walks 3.0 km due north, and then 4.0 km due east. By drawing a vector diagram showing the route, calculate (a) the total distance travelled, [7.0 km] (b) the displacement of the student. [5.0 km at 53° east of north] E4 A sprinter, starting from blocks, reaches his full speed of 9.0 m s −1 in 1.5 s. Determine the sprinter’s average acceleration. [6.0 m s−2] E5 A railway train, travelling along a straight track, takes 1.5 minutes to come to rest from a speed of 115 km h−1. Determine the average acceleration of the train. [−0.35 m s−2] E6 The Earth takes one year to orbit in a circle around the Sun at a distance of 1.5 × 10 11 m. Calculate the average speed and average velocity of the Earth over one year. [30 000 m s−1, 0 m s−1] E7 A racing car accelerates for 10 s through three gear changes with the following average speeds: 20 m s−1 for 2.0 s 40 m s−1 for 2.0 s 60 m s−1 for 6.0 s Determine the average speed of the car during the 10 s acceleration. [48 m s−1]

National Junior College Science Department | Physics 3.1.2 Practice P1 A student walks 8.0 km south-east and then 10 km due west. (a) Draw a vector diagram showing the route. (b) Calculate, using trigonometry, the displacement of the student. P2 A railway train travels at a constant speed of 60 km h −1. It moves e ast for 40 min, then 45° west of north for 30 min. Determine the average velocity of the train. 3.2 DESCRIBING MOTION WITH GRAPHS 3.2.1 Exercises E8 The displacement of a racing car at different times as it travels along a straight track during a time trial is shown below. displacement / m 0 85 170 255 340 time / s 0 1.0 2.0 3.0 4.0 (a) Draw a displacement-time graph for this motion. (b) Determine the velocity of the car. [85 m s−1] E9 The velocity of a motorcyclist at different times as it travels along a straight road during a time trial is shown below. velocity / m s−1 0 15 30 30 20 10 0 time / s 0 5 10 15 20 25 30 (a) Draw a velocity-time graph for this motion. (b) Determine the motorcyclist’s acceleration during the first 10 s. [3.0 m s−2] (c) Determine the motorcyclist’s acceleration during the last 15 s. [−2.0 m s−2] (d) Determine the total distance travelled during the time trial. [525 m] (e) Describe the motion of the motorcycle.

National Junior College Science Department | Physics E10 The graph represents the motion of an object moving with varying acceleration. Estimate the object’s acceleration at P. [20 m s−2] 3.2.2 Practice P3 The graph shows how the velocity of a racing car changes with time. Which statement describes the acceleration? (2009 P1 Q3) A A constant positive acceleration is followed by an acceleration increase and then a negative acceleration. B The acceleration increases positively in the first two sections and then decreases to zero. C The acceleration is positive at the start, increases, then decreases to zero. D The acceleration starts from zero, increases, then decreases to zero.

National Junior College Science Department | Physics P4 The graph shows how the speed of a vehicle varies over a period of time of 150 s. What is the average speed of the vehicle over the 150 s? (2015 P1 Q2) A 10 m s–1 B 12 m s–1 C 14 m s–1 D 16 m s–1 P5 A stone is thrown upwards from the top of a cliff. After reaching its maximum height, it falls past the cliff-top and into the sea. The graph shows how the vertical velocity v of the stone varies with time t after being thrown upwards. R and S are the magnitudes of the areas of the two triangles. What is the height of the cliff-top above the sea? A R B S C R + S D R – S

National Junior College Science Department | Physics P6 A car is travelling along a straight road. The graph shows the variation with time of its acceleration during part of the journey. At what point on the graph does the car have its greatest velocity? P7 The graph shows the variation with time t of the velocity v of a bouncing ball, released from rest. Downward velocities are taken as positive. At which time does the ball reach its maximum height after bouncing? P8 A stone falls freely from rest to the ground. The effects of air resistance on the stone are negligible. The stone travels 0.75 of the total distance to the ground in the last second of its fall. What is the time of the fall? (2014 P1 Q4) A 1.25 s B 1.50 s C 1.67 s D 2.00 s acceleration

National Junior College Science Department | Physics P9 A car accelerates uniformly from rest along a level road. The effects of air resistance on the car are negligible. The car travels 12 m in the time between 1 s and 2 s after starting. How far does it travel in the time between 3 s and 4 s after starting? (2013 P1 Q3) A 28 m B 35 m C 48 m D 64 m P10 The graph below shows the speeds of two cars A and B which are travelling in the same direction over a period of time of 40 s. Car A, travelling at a constant speed of 40 m s −1, overtakes car B at time t = 0. In order to catch up with car A, car B immediately accelerates uniformly for 20 s to reach a constant speed of 50 m s−1. Determine (a) the distance travelled by car A in the first 20 s, [1] (b) the acceleration of car B in the first 20 s, [1] (c) the distance travelled by car B in the first 20 s, [2] (d) the additional time it takes for car B to catch up with car A, [2] (e) the distance each car has travelled since t = 0 when car B catches up with car A, and [1] (f) the maximum distance between the cars before car B catches up with car A. [3] speed / m s–1 time / s40200 0 25 40 50 A B

National Junior College Science Department | Physics P11 An elevator starts at rest on the ninth floor. At t = 0, a passenger pushes a button to go to another floor. The graph below shows the acceleration ay of the elevator as a function of time. Assume positive is upwards acceleration. (a) Sketch a graph of velocity vy of the elevator with time. (b) State and explain if the elevator has gone to a higher or lower floor. ay / m s–2 1/4 0 –1/4 –1/2 t / s vy 0 t / st1 t2 t3 t1 t2 t3 ay / m s−2

National Junior College Science Department | Physics 3.3 UNIFORMLY ACCELERATED LINEAR MOTION 3.3.1 Exercises E11 A car is initially stationary. It has a constant acceleration of 2.0 m s−2. Calculate (a) the velocity of the car after 10 s, [20 m s−1] (b) the distance travelled by the car at the end of 10 s, and [100 m] (c) the time taken by the car to reach a velocity of 24 m s−1. [12 s] E12 A train accelerates steadily from 4.0 m s−1 to 20 m s−1 in 100 s. Calculate (a) the acceleration of the train, [0.16 m s−2] (b) the average velocity of the train, and[12 m s−1] (c) the distance travelled by the train in the 100 s. [1200 m] E13 An egg falls off a table. The floor is 0.80 m from the top of the table. Calculate (a) the time taken to reach the ground, and [0.40 s] (b) the velocity of impact with the ground. [4.0 m s–1] E14 In Section 2.1, we looked at how a motion sensor can be used to measure the speed and position of