Which graph represents the motion of a car that is travelling along a straight road with a speed that increases uniformly with time?

Question 3

Which graph represents the motion of a car that is travelling along a straight road with a speed that increases uniformly with time?

Reference: Past Exam Paper – November 2008 Paper 1 Q8

Solution:

Answer: A. 

We need to look at the axes carefully in each graph so that we can know which quantities are involved and which other quantities may be obtained from the gradient or area under graph.

‘Travelling along a straight road with a speed that increases uniformly with time’ means that there is a uniform acceleration (that is, the acceleration is constant; the acceleration is not changing).

Graph A: Acceleration-time graph – acceleration has a constant value

Graph B: Acceleration-time graph – acceleration is increasing from a non-zero value

Graph C: Displacement-time graph – straight line with a positive gradient à gradient is constant à velocity is constant

Graph D: Displacement-time graph – horizontal line à gradient = 0 à velocity = 0