Show that the rate of change of kinetic energy is a power.

(N/A) The kinetic energy $K$ of an object of mass $m$ moving with velocity $v$ is given by $K = \frac{1}{2}mv^2$.
The rate of change of kinetic energy with respect to time $t$ is given by $\frac{dK}{dt} = \frac{d}{dt}(\frac{1}{2}mv^2)$.
Assuming mass $m$ is constant,we apply the chain rule: $\frac{dK}{dt} = \frac{1}{2}m \cdot 2v \cdot \frac{dv}{dt} = mv \cdot \frac{dv}{dt}$.
Since acceleration $a = \frac{dv}{dt}$,we have $\frac{dK}{dt} = mva$.
By Newton's second law,$F = ma$,so $\frac{dK}{dt} = Fv$.
Power $P$ is defined as the rate of doing work,$P = \frac{dW}{dt} = F \cdot v$.
Thus,the rate of change of kinetic energy is equal to the power delivered by the force,i.e.,$\frac{dK}{dt} = P$.