Question

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

• A. $\upsilon =2s$
• B. $\upsilon =\pm \sqrt{2}s$
• C. $\upsilon =\pm \sqrt{3s}$
• D. $\upsilon =3s$

Answer 1

The correct option is B $\upsilon =\pm \sqrt{2}s$

If $s$ be the displacement , $v$ be the velocity and $a$ be the acceleration then we will have following relation, $a=v\frac{dv}{ds}$

putting $a=2s$ and integrating we get ${\int }_{s=0}^{s}2sds={\int }_{v=0}^{v}vdv$

note-

It was given that velocity$\left(v\right)$ was $zero$ at zero displacement $\left(s\right)$

so we used $v=0$ at $s=0$ in the integration equation above.

after integration we get $s^2=\frac{v^2}{2}$

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