Question

A time varying power $P=2t$ is applied on a particle of mass $m$. Find kinetic energy and velocity of particle as function of time :

• A. $K=t^2,v=\sqrt{\frac{1}{m}}t$
• B. $K=3t^2,v=\sqrt{\frac{2}{m}}t$
• C. $K=t^2,v=\sqrt{\frac{2}{m}}t$
• D. $K=t^2,v=\sqrt{\frac{2}{3m}}t$

Answer 1

The correct option is C $K=t^2,v=\sqrt{\frac{2}{m}}t$

Power supplied to the particle is the rate of change of its kinetic energy.

$⟹\frac{dK}{dt}=2t$

$⟹K=t^2$

$⟹\frac{1}{2}m{v}^2=t^2$

$⟹v=\sqrt{\frac{2}{m}}t$