Question

A particle is moving along a straight line whose velocity-displacement graph is shown in Fig. What is the acceleration is $3m$?

• A. $8\sqrt{3}m{s}^{-2}$
• B. $3\sqrt{3}m{s}^{-2}$
• C. $\sqrt{3}m{s}^{-2}$
• D. $4\sqrt{3}m{s}^{-2}$

Answer 1

The correct option is D $4\sqrt{3}m{s}^{-2}$

$\left(A\right)$

From graph,

$\frac{dv}{ds}=\tan 60$

$=\sqrt{3}$ (Retardation).

We have acceleration, $a=\frac{dv}{dt}$

$\Rightarrow a=\frac{dv}{ds}.\frac{ds}{dt}$

$\Rightarrow a=\frac{dv}{ds}.v$

$\therefore a=\sqrt{3}.4$

$\Rightarrow a=4\sqrt{3}m/s^2$