Work Energy Power

JEE Main level, single correct, medium

147 of 183

Question 147 of 183

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

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Answer: (B) t3/2t^{3 / 2}

P=constant⁡⇒FV= constant ⇒mdVdtV= constant ∫0VVdV=(C)∫0tdt(V22)=CtV∝t1/2dsdt∝t1/2∫0Sds=K∫0tt1/2dtS=K×23t3/2 S∝t3/2\begin{aligned} & P=\operatorname{constant} \Rightarrow \mathrm{FV}=\text { constant } \\ & \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}\end{aligned}
∴\therefore displacement is proportional to (t)3/2(\mathrm{t})^{3 / 2}

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