The velocity of an object changes with time t as shown. Which graph best shows the variation with time t of the displacement s of the object?

Question 18

The velocity of an object changes with time t as shown.

Which graph best shows the variation with time t of the displacement s of the object?

Reference: Past Exam Paper – June 2018 Paper 12 Q5

Solution:

Answer: A.

The gradient of a velocity-time graph gives the acceleration.

The area under a velocity-time graph gives the displacement.

When the velocity is positive, the displacement increases even if the magnitude of the velocity decreases.

e.g. 

if velocity = + 10 m s^-1, the displacement increases by 10 m in each second

if velocity = + 5 m s^-1, the displacement increases by 5 m in each second

The displacement still increases even if the velocity is decreasing (as long as it is positive).

When the velocity is negative, the displacement decreases. [B and C are incorrect]

Now, the gradient of a displacement-time graph gives the velocity.

Graph D gives a constant gradient for the increase and a constant gradient for the decrease. This implies that during the increase, the velocity is constant – it is not changing. But this is incorrect as we can see from the graph that the velocity DECREASES from a maximum value to zero for the first section. [D is incorrect]

So, graph A is the correct choice as it shows a decreasing gradient for the first section (indicating a decreasing velocity) and an increasing but negative gradient in the second section (indicating a velocity increasing in the negative direction).