A body of mass $m$, accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power…

A body of mass $m$, accelerates uniformly from rest to $v_1$ in time $t_1$. The instantaneous power delivered to the body as a function of time $t$ is
  1. $\frac{\mathrm{mv}_1 \mathrm{t}}{\mathrm{t}_1}$
  2. $\frac{\mathrm{mv}_1^2 \mathrm{t}}{\mathrm{t}_1^2}$
  3. $\frac{m v_1 t^2}{t_1}$
  4. $\frac{m v_1^2 t}{t_1}$

Solution

Power $P=\vec{F} \cdot \vec{v}=\operatorname{mav}=m\left(\frac{v_1}{t_1}\right)\left(\frac{v_1}{t_1} t\right)=\frac{m_1^2 t}{t_1^2}$

Asked in: JEE Main 2004

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