Question

A boy is moving unidirectionally under the influence of constant power source. Its displacement in time '$t$' is proportional to

• A. $t^{\frac{1}{2}}$
• B. $t$
• C. $t^{\frac{3}{2}}$
• D. $t^2$

Answer 1

The correct option is C $t^{\frac{3}{2}}$

$P=\left(m\frac{dv}{dt}\right)v\Rightarrow \int Pdt=\int mvdv\Rightarrow Pt=\frac{1}{2}m{v}^2\Rightarrow v=\left(\sqrt{\frac{2P}{m}}\right)\sqrt{t}\Rightarrow \frac{ds}{dt}=\left(\sqrt{\frac{2P}{m}}\right)\sqrt{t}\Rightarrow \int ds=\left(\sqrt{\frac{2P}{m}}\right)\int \sqrt{t}dt\Rightarrow s=\left(\sqrt{\frac{2P}{m}}\right)\frac{t^{\frac{3}{2}}}{\frac{3}{2}}$