Question

A body is moving unidirectionally under the influence of a force 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 $t^{3/2}$

Let the constant power be $P$

Initial velocity $=0$

Also, $P=Fv=mav$

Thus, $P=m{a}^{2}t$

So, $a=\sqrt{\frac{P}{mt}}$

As we know, $S=ut+\frac{1}{2}a{t}^2$

Thus, $S=\frac{1}{2}\sqrt{\frac{P}{mt}}\times t^2$

Thus, $S=\frac{1}{2}\sqrt{\frac{P}{m}}\times t^{\frac{3}{2}}$

$⟹S\propto t^{\frac{3}{2}}$