A bus takes a time of 25 s to reach a constant speed while travelling in a straight line. A graph of speed v against time t is shown.

Question 12

A bus takes a time of 25 s to reach a constant speed while travelling in a straight line. A graph of speed v against time t is shown.

Which graph shows the variation with t of the resultant force F on the bus?

Reference: Past Exam Paper – November 2015 Paper 12 Q10

Solution:

Answer: A.

Resultant force F = ma

The resultant force is proportional to the acceleration.

From the velocity-time graph, the acceleration can be obtained from the gradient.

Time t = 0 to t = 5s: constant gradient, so the acceleration is constant (and thus, the force is also constant) [B, C and D are incorrect]

Time t = 5s to t = 10s: gradient is constant (same as before), then the line becomes steeper indicating a greater value of gradient. So, the acceleration (and the force) increases from one constant value to a greater constant value (as shown in A).

Time t = 10s to t = 55s: constant gradient, so the acceleration (and force) is constant (same as just before)

Time t = 15s to t = 25s: decreasing gradient, so the acceleration (and force) is decreasing