Q#18 (Past Exam Paper – June 2018 Paper 12 Q5)
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?
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).
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