Question

The rate of change of kinetic energy is $n$ times ($n$ is constant with appropriate dimension) the velocity at any moment of a particle of mass $m$, which starts moving in a straight line. The constant acceleration with which particle is moving is

• A. $mn$
• B. $\frac{m}{n}$
• C. $\frac{n}{m}$
• D. $\frac{1}{mn}$

Answer 1

The correct option is C $\frac{n}{m}$

$K=\frac{1}{2}m{v}^2$

$\frac{dK}{dt}=mv\times \frac{dv}{dt}=m\frac{dv}{dt}v=mav,\Rightarrow mav=nv$

$ma=n,a=\frac{n}{m}$