Exercises: Acceleration and velocity–time graphs

Define acceleration and state its unit in the SI.

A cyclist on the Dublin quays increases her speed from 2 m/s to 8 m/s in 3 s. Use $a = \dfrac{v-u}{t}$ to calculate her acceleration.

A velocity–time graph for a car is a horizontal straight line at 20 m/s from 0 s to 10 s.

1. a) Describe the motion of the car.

1. b) What is its acceleration?

A train leaves Limerick station and its velocity increases uniformly from 0 to 24 m/s in 30 s.

1. a) Calculate its acceleration.

1. b) The train then travels at 24 m/s for 60 s. How far does it travel in this time?

1. c) Describe the shape of the velocity–time graph for the whole 90 s.

A velocity–time graph of a runner has these points: (0 s, 0 m/s), (4 s, 8 m/s), (10 s, 8 m/s), (14 s, 0 m/s).

1. a) Calculate the acceleration during the first 4 s.

1. b) Describe the motion between 4 s and 10 s.

1. c) Calculate the acceleration between 10 s and 14 s and explain the meaning of its sign.

A car travelling at 25 m/s brakes and stops in 5 s.

1. a) Calculate its acceleration.

1. b) Use the area under the velocity–time graph to find the distance travelled while braking.

1. c) Explain why the answer to a) is negative.

A velocity–time graph of a bus has these points: (0 s, 0 m/s), (10 s, 15 m/s), (40 s, 15 m/s), (50 s, 0 m/s).

1. a) Calculate the acceleration in each of the three stages.

1. b) Calculate the total distance travelled using areas under the graph.

1. c) Calculate the average speed for the whole journey.

Two cars, A and B, start from rest. Car A reaches 30 m/s in 10 s. Car B reaches 24 m/s in 6 s. Both accelerate uniformly.

1. a) Which car has the greater acceleration? Show your calculations.

1. b) Which car is travelling faster after 6 s? Justify your answer.

1. c) Sketch in words how the two velocity–time graphs would differ.

A student states: "On a velocity–time graph, a line that slopes downwards means the object is going backwards." The line goes from (0 s, 12 m/s) to (6 s, 3 m/s).

1. a) Evaluate the student's statement.

1. b) Calculate the acceleration.

1. c) Calculate the distance travelled in the 6 s.

1. d) Describe what the graph would show if the object did reverse direction.