Question

A body starts from rest with uniform acceleration and acquires a velocity V in time T. The instantaneous kinetic energy of the body after any time t is proportional to:

• A. $\left(V/T\right)t$
• B. $\left(V^2/T\right)t^2$
• C. $\left(V^2/T^2\right)t$
• D. $\left(V^2/T^2\right)t^2$

Answer 1

The correct option is D $\left(V^2/T^2\right)t^2$

Here,
$u=0$
$V=0+at$

Hence, $a=V/T$
$KE=0.5m{v}^2$
$v=at=Vt/T$
$K{E}_t=0.5m(V/T{)}^2$

Hence, $KE\propto \frac{V^2{t}^2}{T^2}$