Question

The displacement-time graph for two particles A and B are straight lines inclined at angles of ${30}^{\circ }$ and ${60}^{\circ }$ with the time axis. The ratio of velocities of $V_A$ : $V_B$ is

• A. 1 : 2
• B. 1 : $\sqrt{3}$
• C. $\sqrt{3}$ : 1
• D. 1 : 3

Answer 1

The correct option is D

1 : 3

The slope is given by $tan\theta$. Therefore,

$\frac{V_A}{V_B}=\frac{\tan {\theta }_A}{\tan {\theta }_B}=\frac{\tan {30}^{\circ }}{\tan {60}^{\circ }}=\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}}=\frac{1}{3}$