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 $1:3$

As velocity, $v=\frac{dx}{dt}$, it is the slop of displacement-time graph
So, $\frac{V_A}{V_B}=\frac{slop{e}_A}{slop{e}_B}$
And $slope=\tan \theta$
So, $\frac{V_A}{V_B}=\frac{\tan {30}^{\circ }}{\tan {60}^{\circ }}=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}$