A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $\mathrm{t}$ is proportional to :

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Aicharya · Accepted Answer

$\begin{aligned} & P=\operatorname{constant} \Rightarrow \mathrm{FV}=	ext { constant } \ & \Rightarrow \mathrm{m} \frac{\mathrm{dV}}{\mathrm{dt}} \mathrm{V}=	ext { constant } \ & \int_0^{\mathrm{V}} \mathrm{VdV}=(\mathrm{C}) \int_0^{\mathrm{t}} \mathrm{dt} \ & \left(\frac{\mathrm{V}^2}{2}ight)=\mathrm{Ct} \ & \mathrm{V} \propto \mathrm{t}^{1 / 2} \ & \frac{\mathrm{ds}}{\mathrm{dt}} \propto \mathrm{t}^{1 / 2} \ & \int_0^{\mathrm{S}} \mathrm{ds}=\mathrm{K} \int_0^{\mathrm{t}} \mathrm{t}^{1 / 2} \mathrm{dt} \ & \mathrm{S}=\mathrm{K} 	imes \frac{2}{3} \mathrm{t}^{3 / 2} \ & \mathrm{~S} \propto \mathrm{t}^{3 / 2}\end{aligned}$ $	herefore$ displacement is proportional to $(\mathrm{t})^{3 / 2}$

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time…

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