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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
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$\frac{\mathrm{mv}_1^2 \mathrm{t}}{\mathrm{t}_1^2}$
$\frac{\mathrm{mv}_1^2 \mathrm{t}}{\mathrm{t}_1^2}$
Power $P=\vec{F} \cdot \vec{v}=\operatorname{mav}=m\left(\frac{v_1}{t_1}\right)\left(\frac{v_1}{t_1} t\right)=\frac{m_1^2 t}{t_1^2}$
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