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

The correct option is C $t^{3/2}$

$P=k=$ constant
$Fv=k$
$mav=k$
$m{\int }_0^{v}vdv=k{\int }_0^{t}dt$
$\frac{m{v}^2}{2}=kt$
$\Rightarrow v=\sqrt{\frac{2kt}{m}}$
${\int }_0^{x}dx=\sqrt{\frac{2k}{m}}{\int }_0^t\sqrt{t}dt$
$x=\sqrt{\frac{2k}{m}}\times \frac{2t^{3/2}}{3}$
$\Rightarrow x\propto t^{\frac{3}{2}}$