Question

The displacement-time graphs of two bodies $A$ and $B$ are shown in figure. The ratio $\left(\frac{v_{A}}{v_{B}}\right)$ of velocity of $A$ to velocity of $B$, is

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

Answer 1

Answer: (C)

Velocity is defined as rate of change of displacement $(s)$.
$\therefore v=\frac{\Delta s}{\Delta t}$
In the given graph,

Rate of change of displacement
= slope of $s$-t graph
$ = \tan \theta$
$\therefore \tan 60^{\circ}=\frac{B D}{O D}=v_{B}$
$\tan 30^{\circ}=\frac{A C}{O C}=v_{A}$
$\therefore \frac{\tan 60^{\circ}}{\tan 30^{\circ}}=\frac{v_{B}}{v_{A}}$
$\Rightarrow \frac{v_{B}}{v_{A}}=\frac{\sqrt{3}}{1 / \sqrt{3}}=\frac{3}{1}$
$\therefore v_{A}: v_{B}=1: 3$