Question

The acceleration of a particle moving in a straight line varies with its displacement as, $a=2s$ velocity of the particle is zero at zero displacement. Find the corresponding velocity displacement equation.

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

Answer 1

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

Given,

$a=2s$

Acceleration of body is given as,

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

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

$2sds=vdv$

Integrating both side to obtain the value of speed:

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

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

$v^2=2s^2$

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

$v=s\sqrt{2}$

The correct option is A.