Question

The displacement time graphs of two particles A and B are straight lines making angles of respectively ${30}^o$ and ${60}^o$ with the time axis. If the velocity of A is $v_A$ and that of B is $v_B$, then the value of $\frac{v_A}{v_B}$ is:

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

Answer 1

The correct option is D $\frac{1}{3}$

Slope of displacement-time graph gives the instantaneous velocity of the body.

Slope of particle A $=\tan {30}^o$

Slope of particle B $=\tan {60}^o$

So, ratio of velocity $\frac{V_A}{V_B}=\frac{\tan {30}^o}{\tan {60}^o}=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}$