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^1/2
• B. t^3/4
• C. t^3/2
• D. t²

Answer 1

The correct option is C t^3/2

$P=Fv=mav=m(\frac{dv}{dt})v\Rightarrow \frac{P}{m}dt=vdv$
$\Rightarrow \frac{P}{m}\times t=\frac{v^2}{2}\Rightarrow v=(\frac{2P}{m}{)}^{\frac{1}{2}}(t{)}^{\frac{1}{2}}$
Now $s=\int vdt=\int (\frac{2P}{m}{)}^{\frac{1}{2}}{t}^{\frac{1}{2}}dt$
$\therefore s=(\frac{2P}{m}{)}^{\frac{1}{2}}[\frac{2t^{\frac{3}{2}}}{3}]\Rightarrow s\propto t^{\frac{3}{2}}$