Question

The velocity-position graph of a particle moving in a straight line varies with its displacement as $a=2s$ velocity of particle is zero at zero displacement$.$ The corresponding velocity displacement equation is

• A. $\pm \sqrt{2}s$
• B. $\sqrt{2s}$
• C. $v^2=\frac{2}{s}$
• D. $v=\pm \frac{2}{s}$

Answer 1

The correct option is A $\pm \sqrt{2}s$

$a=2s$

$v\frac{dv}{ds}=2s$

$vdv=2sds$

${\int }_0^{v}vdv={\int }_0^{s}2sds$

$\frac{v^2}{2}=s^2$

$v=\pm \sqrt{2}s$

Hence,

option $\left(A\right)$ is correct answer.