As a train travels 500 m its speed increases from 5 \displaystyle \text{m}{{\text{s}}^{-1}} to 15 \displaystyle \text{m}{{\text{s}}^{-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.

Answer

Answer 6.4

Solution a

Solution 6.4a

Solution b

Solution 6.4b

Exercise 6.5

A cyclist accelerates at 0.5 \displaystyle \text{m}{{\text{s}}^{-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 \displaystyle \text{m}{{\text{s}}^{-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.

Answer

Answer 6.5

Solution a

Solution 6.5a

Solution b

Solution 6.5b

Exercise 6.6

As a van travels along a straight road its speed increases from 9 \displaystyle \text{m}{{\text{s}}^{-1}} to 24 \displaystyle \text{m}{{\text{s}}^{-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.

Answer

Answer 6.6

Solution a

Solution 6.6a

Solution b

Solution 6.6b

Exercise 6.7

A vehicle accelerates uniformly from 6 \displaystyle \text{m}{{\text{s}}^{-1}} to 19 \displaystyle \text{m}{{\text{s}}^{-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.

Answer

Answer 6.7

Solution a

Solution 6.7a

Solution b

Solution 6.7b

Exercise 6.8

As a lift descends, it accelerates at a constant rate from rest until it reaches a speed of 0.6 \displaystyle \text{m}{{\text{s}}^{-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.

Answer a

Answer b

Answer c

Solution a

Solution b

Solution c

Exercise 6.9

A car decelerates from a velocity of 36 \displaystyle \text{m}{{\text{s}}^{-1}}. The magnitude of the deceleration is \displaystyle 3\ \text{m}{{\text{s}}^{-2}}. Calculate the time required for the car to travel a distance of 162 m.

Answer

Answer 6.9

Solution

Solution 6.9

Exercise 6.10

A sprinter starts from rest, and accelerates at 2 \displaystyle \text{m}{{\text{s}}^{-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.

Answer a

Answer b

Answer c

Solution a

Solution b

Solution c