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.
• B.
• C.
• D.

Answer 1

The correct option is C

$P=Fv=mav=m(\frac{dv}{dt})v\Rightarrow \frac{P}{m}dt=vdv$

$\Rightarrow \frac{P}{m}\times t=\frac{v^2}{2}\Rightarrow v=(\frac{2P}{m}{)}^{\frac{1}{2}}(t{)}^{\frac{1}{2}}$

Now s = $\int vdt=\int (\frac{2P}{m}{)}^{\frac{1}{2}}(t{)}^{\frac{1}{2}}dt$

$\therefore s=(\frac{2P}{m}{)}^{\frac{1}{2}}[\frac{2t^{3}2}{3}]\Rightarrow s\infty (t{)}^{\frac{3}{2}}$