Question

derive an expression to find power in terms of force and velocity

Answer 1

The power at a particular instant of time t is the ratio of small work done(dW) to the small time interval (dt) around t,i.e.,
P = dW/dt
Now, dW = $\overrightarrow{F}.d\overrightarrow{s},where\overrightarrow{F}$ is the force applied and $d\overrightarrow{s}$ is the small displacement.
$$\begin{gathered} P=\frac{\overrightarrow{F}.d\overrightarrow{s}}{dt} \\ But\frac{d\overrightarrow{s}}{dt}=\overrightarrow{v} \\ So,P=\overrightarrow{F}.\overrightarrow{v} \end{gathered}$$