A body is moving unidirectionally under the influence of a constant Power source. Its displacement in time \(t\) is proportional to _______.

\(\Rightarrow \mathrm{m} \frac{\mathrm{dV}}{\mathrm{dt}} \mathrm{V}=\text { constant }\)

\(\int_0^{\mathrm{V}} \mathrm{VdV}=(\mathrm{C}) \int_0^{\mathrm{t}} \mathrm{dt}\)

\(\left(\frac{\mathrm{V}^2}{2}\right)=\mathrm{Ct}\)

\(\mathrm{V} \propto \mathrm{t}^{1 / 2}\)

\(\frac{\mathrm{ds}}{\mathrm{dt}} \propto \mathrm{t}^{1 / 2}\)

\(\int_0^{\mathrm{s}} \mathrm{ds}=\mathrm{K} \int_0^{\mathrm{t}} \mathrm{t}^{1 / 2} \mathrm{dt}\)

\(\mathrm{S}=\mathrm{K} \times \frac{2}{3} \mathrm{t}^{3 / 2}\)

\(\mathrm{~S} \propto \mathrm{t}^{3 / 2}\)

\(\therefore \text { displacement is proportional to }(\mathrm{t})^{3 / 2}\)