Question

A ball 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)

$t^{3/2}$

Here, power $P=Fv=mav$
$P=mv\frac{dv}{dt}=$ constant (say $k$)
$\therefore vdv=\frac{k}{m}dt$
On intergration, we get
$\frac{v^2}{2}=\frac{k}{m}t$
$\Rightarrow v=\sqrt{\frac{2k}{m}}.t^{1/2}$
$\therefore \frac{ds}{dt}=\sqrt{\frac{2k}{m}}.t^{1/2}$
$ds=k^{{}^{\prime }}{t}^{1/2}dt$
On integration we get $s=\frac{2}{3}{k}^{{}^{\prime }}{t}^{3/2}$
$\Rightarrow s\propto t^{3/2}$