Question

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

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

Answer 1

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

$Power=\frac{w}{t}=\frac{\frac{1}{2}m{v}^2}{t}=constant$
$\therefore$ $v^2\propto t$
$v^2\propto t$
$v\propto t^{1/2}$
$\therefore$ Displacement(magnitude)= Velocity x Time
$=v\times t$ $\propto t^{1/2}\times t=t^{3/2}$