Q. The kinetic energy $K$ of a particle moving in straight line depends upon the distance $s$ as : $K = as^{2}$ The force acting on the particle is
A) $2\ as$
B) $2\ mas$
C) $2a$
D) $\sqrt{as^{2}}$
Explanation
(a) Given, $K = as^{2}$ or $\frac{1}{2}mv^{2} = as^{2}$
or $mv^{2} = 2as$
Differentiating w.r.t. time $t$,
$m.(2v).\left( \frac{dv}{dt} \right) = (2a)(2s)\left( \frac{ds}{dt} \right)$
$\therefore\ \frac{ds}{dt} = v$
$\therefore\ \ 2m\frac{dv}{dt} = 4as \Rightarrow m\frac{dv}{dt} = 2as$
or $F_{t} = 2as$
$F = \sqrt{F_{t}^{2} + F_{r}^{2}}\ \ \ \ (\therefore F_{r} = 0)$
$F = F_{t} = 2as$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.