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Q.
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
Work, Energy and Power
Solution:
Acceleration $a=\frac{v_{1}}{t_{1}}$
$\therefore $ velocity $(v)=0+a t=\frac{v_{1}}{t_{1}} t$
$\therefore $ Power $P=$ Force $\times$ velocity $=m a v$
or $ P=m\left(\frac{v_{1}}{t_{1}}\right) \times\left(\frac{v_{1} t}{t_{1}}\right)=\frac{m v_{1}^{2} t}{t_{1}^{2}}$.