Question

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

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

Answer 1

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

Let $m$ be the mass of the body.

Given: $P=$ constant

Applying work- energy theorem,

$\frac{1}{2}m{v}^2-0=Pt$

$\Rightarrow v=\sqrt{\frac{2P}{m}}\sqrt{t}$

$\Rightarrow \frac{dx}{dt}=C\sqrt{t}(C=\sqrt{\frac{2P}{m}}=\text{constant})$

$\Rightarrow dx=C\sqrt{t}dt$

After integrating , we get

$x=C\times \frac{t^{3/2}}{3/2}$

$\therefore x\propto t^{3/2}$

Hence, option $\left(\text{A}\right)$ is correct.