Question

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

• A. $t^{1/2}$
• B. $t$
• C. $t^{3/2}$
• D. $t^2$

Answer 1

Answer: (C)

Let $s=K{t}^n$, where $K$ is a constant $v=\frac{ds}{dt}=nK{t}^{n-1}$
$a=\frac{d^{2}s}{d{t}^2}=n(n-1)K{t}^{n-2}$
Now, $P=Fv=(ma)(v)$
$P=m\left[n(n-1)K{t}^{n-2}\right]\cdot \left(nK{t}^{n-1}\right)$
If power $P$ is constant, then it must be independent of time $t$.
$\Rightarrow t^{2n-3}=t^0$ or $2n-3=0$ or $n=\frac{3}{2}$