Power is defined as the rate at which work is done.
Power = Work done / time
Its unit is watt and dimensional formula is ML2T-3.
Power is said to be one watt, when one joule of work is said to be done in one second.
If dw is the work done during an interval of time dt then,
Power = dw/dt … … (1)
But, dw = (F cos θ) ds … …. (2)
where θ is the angle between the direction of the force and displacement. F cos θ; is component of the force in the direction of the small displacement ds.
Substituting equation (2) in (1); power = [(F cos θ) ds] /dt
= (F cosθ) (ds/dt) = (F cosθ).v (we know ds/dt = v)
So, power = (F cos θ).v
If F and v are in the same direction, then power = F cos θ = Fv = Force x velocity
It is also represented by the dot product of F and v.
Then; P = F . v