The velocity-time graph shows the motion of a scooter along a straight road for 14 s.
Find the acceleration of the scooter in the first 4 s.
Find the deceleration of the scooter in the last 4 s.
Find the total distance travelled by the scooter.
4 marks
Show answer
a) 3 m s-2b) 3 m s-2c) 120 m
2
The displacement-time graph shows a dog running away from its owner along a straight path and then back again.
Find the velocity of the dog in the first 40 s.
Describe the motion of the dog between t = 40 and t = 60
Find the velocity of the dog between t = 60 and t = 100
Find the average speed and the average velocity of the dog for the whole 100 s.
4 marks
Show answer
a) 1.5 m s-1b) at rest, 60 m from the ownerc) -1.5 m s-1 (1.5 m s-1 back towards the owner)d) average speed 1.2 m s-1, average velocity 0
3
A car starts from rest and accelerates uniformly to 20 m s−1 in 8 s. It travels at 20 m s−1 for 20 s and then decelerates uniformly to rest in 5 s.
Sketch a speed-time graph for the journey on the axes.
Find the total distance travelled.
4 marks
Show answer
a) straight lines from (0, 0) to (8, 20), (8, 20) to (28, 20), (28, 20) to (33, 0)b) 530 m
4
A train starts from rest at a station and accelerates uniformly to 16 m s−1 in 20 s. It then travels at 16 m s−1 for T seconds and then decelerates uniformly to rest at the next station in 12 s. The speed-time graph is shown. The distance between the stations is 1600 m.
Find the value of T.
5 marks
Show answer
T = 84
5
A cyclist passes a point A with speed 4 m s−1. She accelerates uniformly for 10 s to a speed of V m s−1, and then travels at this speed for a further 30 s, when she reaches the point B. The distance AB is 405 m. The speed-time graph is shown.
Find the value of V.
Find the acceleration of the cyclist in the first 10 s.
6 marks
Show answer
a) V = 11b) 0.7 m s-2
6
A tram starts from rest and accelerates uniformly at 0.8 m s−2 until it reaches a speed of 20 m s−1. It travels at this speed and then decelerates uniformly at 0.5 m s−2 until it stops. The whole journey takes 200 s.
Sketch a speed-time graph for the journey.
Find the time for which the tram travels at constant speed.
Find the total distance travelled.
6 marks
Show answer
a) lines from (0, 0) to (25, 20), flat to (160, 20), down to (200, 0)b) 135 sc) 3350 m
7
Car A moves along a straight road at a constant speed of 15 m s−1. At time t = 0 it passes car B, which is at rest. At that instant B sets off in the same direction, accelerating uniformly to 25 m s−1 in 10 s and then keeping this speed. The velocity-time graphs of both cars are shown.
Find the time at which the cars have the same speed.
Find the greatest distance by which A is ahead of B.
Find the time at which B overtakes A.
7 marks
Show answer
a) t = 6 sb) 45 mc) t = 12.5 s
8
The velocity-time graph shows the motion of a particle moving along a straight line for 8 s.
Find the acceleration of the particle in the first 6 s.
Find the displacement of the particle from its starting point after 8 s.
Find the total distance travelled by the particle in the 8 s.
6 marks
Show answer
a) -2 m s-2b) 4 mc) 28 m
9
A car starts from rest at A and accelerates at 2 m s−2 until it reaches a speed of V m s−1. It then immediately decelerates at 3 m s−2 until it stops at B. The distance AB is 240 m.
Sketch a speed-time graph for the motion.
Find, in terms of V, the total time from A to B.
Find the value of V and the total time.
6 marks
Show answer
a) a triangle: straight up to V at t = V/2, then straight down to 0 at t = 5V/6b)5V6 sc) V = 24, total time 20 s
10
A lift rises from rest. It accelerates uniformly at 1.2 m s−2 for 2.5 s, then moves at constant speed, and then decelerates uniformly to rest in 2 s. The lift rises 45 m in total.
Find the greatest speed of the lift.
Sketch a speed-time graph for the motion of the lift.
Find the time for which the lift moves at constant speed, and the total time for the journey.
6 marks
Show answer
a) 3 m s-1b) up to (2.5, 3), flat to (15.25, 3), down to (17.25, 0)c) 12.75 s at constant speed, 17.25 s in total
11
A train travels between two stations 3000 m apart. It starts from rest and accelerates uniformly at 0.6 m s−2 until it reaches a speed of V m s−1. It travels at this speed and then decelerates uniformly at 0.9 m s−2 until it comes to rest at the second station. The whole journey takes 180 s. The speed-time graph is shown.
Show that the total time spent accelerating and decelerating is 25V9 seconds.
Show that 25V2 − 3240V + 54000 = 0
Find the value of V, explaining why you reject the other solution.
9 marks
Show answer
a)5V3 + 10V9 = 25V9 shownb) 25V2 - 3240V + 54000 = 0 shownc) V = 19.6 (the other root, 110, would need longer than 180 s to speed up and slow down)
12
In a model of a 100 m race, a sprinter starts from rest, accelerates uniformly for 3 s to a speed of V m s−1, and then runs at constant speed V m s−1 to finish the race in 11 s.
Sketch a speed-time graph for the model.
Find the value of V.
Find the acceleration of the sprinter in the first 3 s.
Give two reasons why the model may not be realistic.
8 marks
Show answer
a) straight line from (0, 0) to (3, V), then horizontal to (11, V)b) V = 10.5 (10.526...)c) 3.51 m s-2d) the acceleration would not be constant, the change from accelerating to constant speed would not be sudden, and a real sprinter slows down near the end of the race
Every question here is original and written by Robinson Tuition. It follows the Edexcel AS specification and suits AQA and OCR AS maths too; this is not an exam-board paper.