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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Solution

consider the acceleration 'a' is constant
from the equation $V = U + a t$
$V_{1} = 0 + a t_{1}$
$a = \frac{V_{1}}{t_{1}}$
at any instant 't' the velocity of the body 'V' is
$V = 0 + a t ⟹ V = a t$
now $V = \frac{V_{1}}{t_{1}} \times t$
power = $F \times V = m a \times V$
$P = m (\frac{V_{1}}{t_{1}}) \times [\frac{V_{1}}{t_{1}} \times t]$ = $\frac{m {V_{1}}^{2} t}{{t_{1}}^{2}}$

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