A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power…

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function time is given by
  1. $\frac{\mathrm{mv}^2}{\mathrm{~T}^2} \cdot \mathrm{t}$
  2. $\frac{m v^2}{T^2} \cdot t^2$
  3. $\frac{1}{2} \frac{\mathrm{mv}^2}{\mathrm{~T}^2} \cdot \mathrm{t}$
  4. $\frac{1}{2} \frac{\mathrm{mv}^2}{\mathrm{~T}^2} \cdot \mathrm{t}^2$

Solution

$\mathrm{P}=(\mathrm{ma}) \cdot \mathrm{v}$ $=m a^2 t$ $=m \frac{V^2}{T^2} t$

Asked in: JEE Main 2005

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