Q. A car starts from station and moves along the horizontal road by a machine delivering constant power. The distance covered by the car in time $t$ is proportional to
A) $t^{2}$
B) $t^{3/2}$
C) $t^{2/3}$
D) $t^{3}$
Explanation
(b) Power, $P = \frac{W}{t}$
$P = \frac{Fs}{t},P = \frac{mas}{t}$ $(\because F = ma)$
$P = \frac{mv\ s}{t^{2}},$ $\left( \because a = \frac{v}{t} \right)$
$P = \frac{ms \bullet s}{t^{3}}$ $\left( \because v = \frac{s}{t} \right)$
$Pt^{2} = ms^{3}$
$\therefore\ s \propto t^{3/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.