Question

A body is moving 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)

$t^{3/2}$

Since the power is constant we have $P=W/t=constant=k$
or
$W=Fx=kt=m\left(\frac{dv}{dt}\right)x=kt$
Integrating
$mvx=k{t}^2$
or
$m\left(\frac{dx}{dt}\right)x=k{t}^2$
Integrating again we have
$m\frac{x^2}{2}=\frac{k{t}^3}{3}$
Thus we get
$x\propto t^{3/2}$