Question

Two straight lines drawn on the same displacement - time graph make an ${30}^{\circ }$ and ${60}^{\circ }$ with time axis respectively as shown in fig-1. What is the ratio of the two velocities?

Answer 1

Velocity is given by: $V=\frac{displacement}{time}$

Velocity, $V=\tan \alpha$

Ratio of two velocities $=\frac{\tan 30}{\tan 60}=\frac{\sqrt{3}}{3}\times \frac{1}{\sqrt{3}}=\frac{1}{3}$