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Q.
A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to
Work, Energy and Power
Solution:
Let $s=K t^{n}$, where $K$ is a constant $v=\frac{d s}{d t}=n K t^{n-1}$
$a=\frac{d^{2} s}{d t^{2}}=n(n-1) K t^{n-2}$
Now, $P=F v=(m a)(v)$
$P=m\left[n(n-1) K t^{n-2}\right] \cdot\left(n K t^{n-1}\right)$
If power $P$ is constant, then it must be independent of time $t$.
$\Rightarrow t^{2 n-3}=t^{0}$ or $2 n-3=0$ or $n=\frac{3}{2}$