Question

A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time $t$ is proportional to:

• A. $t^{1/2}$
• B. $t^{3/4}$
• C. $t$
• D. $t^{3/2}$

Answer 1

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

Using the formula, $S=ut+\frac{1}{2}a{t}^2$

As the body is at rest so $u=0$.

The distance moved by body is $S=\frac{1}{2}a{t}^2$

Power $=$ force $\times$ velocity or $p=Fv=ma\times \left(at\right)$ (using $v=u+at,v=0+at$)

or $p=m{a}^{2}t$

So, $S=0.5\sqrt{p/m}{t}^{-1/2}{t}^2$ or $S\propto t^{3/2}$