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
$=\tan \theta$
$\therefore \tan 60^{\circ }=\frac{BD}{OD}=v_B$
$\tan 30^{\circ }=\frac{AC}{OC}=v_A$
$\therefore \frac{\tan 60^{\circ }}{\tan 30^{\circ }}=\frac{v_B}{v_A}$
$\Rightarrow \frac{v_B}{v_A}=\frac{\sqrt{3}}{1/\sqrt{3}}=\frac{3}{1}$
$\therefore v_A:v_B=1:3$