A mass on the end of a spring bounces up and down as shown, after being released at time t = 0.

Question 25

A mass on the end of a spring bounces up and down as shown, after being released at time t = 0.

Which graph shows how the velocity varies with time?

Reference: Past Exam Paper – November 2012 Paper 13 Q10

Solution:

Answer: A.

From the distance-time graph, the velocity may be obtained by the gradient.

When the gradient is positive, the velocity is up even if the distance on the graph is down.


The distance-time graph can be broken down into 4 sections, separated by the marks on the x-axis.

In the first section, the gradient is positive and increasing. So, the velocity is up and increasing.

In the second section, the gradient is positive and decreasing. So, the velocity is still up but decreasing.

In the beginning of the third section the gradient is zero, so the velocity is zero. The gradient is negative and increasing. So, the velocity is down and increasing.
 
In the last section, the gradient is still negative but decreasing. So, the velocity is down and decreasing.