6. Exercises

The graph shows how the velocity of a van changes during a short journey. Find the distance travelled by the van.

The graph below shows how the velocity of a train changes as it travels along a straight railway line.

a) Find the total distance travelled by the train in the 180 seconds..

b) Find the acceleration of the train on the first stage of the motion.

The diagram shows a velocity-time graph for a lift.

a) Find the total distance travelled by the lift.

b) Calculate the acceleration of the lift during the last 2 seconds.

c) At what times is the speed of the lift 1 ms−1?

As a train travels 500 m its speed increases from 5 ms−1 to 15 ms−1. Assume that its acceleration is constant.

a) Find the acceleration of the train.

b) Find the time it takes the train to travel this distance.

A cyclist accelerates at 0.5 ms−2 from rest for 10 seconds, as she travels along a straight line.

a) Find the distance travelled by the cyclist during the 10 seconds and the speed that she reaches at the end of this period of time.

b) After the 10 seconds her acceleration changes to 0.2 ms−2 and then remains constant for a further 5 seconds. Find the speed of the cyclist and the total distance that she has travelled at the end of the 15 seconds.

As a van travels along a straight road its speed increases from 9 ms−1 to 24 ms−1 as it travels 495 m.

a) Find the acceleration of the van.

b) Find the time taken by the van to travel the 495 m.

A vehicle accelerates uniformly from 6 ms−1 to 19 ms−1, in a 20 second period of time, as it travels in a straight line.

a) Find the acceleration of the vehicle.

b) Find the distance travelled by the vehicle.

As a lift descends, it accelerates at a constant rate from rest until it reaches a speed of 0.6 ms−1 after 8 seconds.

a) Find the acceleration of the lift.

b) The lift continues to accelerate for a further 2 seconds. Find the distance that the lift has now travelled.

c) The lift then slows down, at a constant rate, and stops after a further 5 seconds. Find the total distance travelled by the lift.

A car decelerates from a velocity of 36 ms−1. The magnitude of the deceleration is 3 ms−2. Calculate the time required for the car to travel a distance of 162 m.

A sprinter starts from rest, and accelerates at 2 ms−2 for the first 4 seconds of a race. Assume that the sprinter moves along a straight line.

a) Find the distance travelled by the sprinter in the first 4 seconds.

b) Find the speed of the sprinter at the end of the first 4 seconds.

c) The sprinter then travels at this constant speed for the rest of the race. He travels a total distance of 100 metres. Find the total time that he takes to complete the race.