Question

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

Answer 1

Answer: (C)

$t^{3/2}$

Answer 2

P = constant
$\therefore$ Work done in time t.
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, W = Pt$
From work-energy theorem, net work done is change in kinetic energy. Therefore,
$\frac{1}{2} mv^2=pt$
or $\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, v \propto t^{1/2}$
Integrating, we get $s \propto t^{3/2}$