In physics, power is the rate at which work is performed or energy is converted
If ΔW is the amount of work performed during a period of time of duration Δt, the average power Pavg over that period is given by the formula
It is the average amount of work done or energy converted per unit of time. The average power is often simply called “power” when the context makes it clear.
The instantaneous power is then the limiting value of the average power as the time interval Δt approaches zero.
In the case of constant power P, the amount of work performed during a period of duration T is given by:
In the context of energy conversion it is more customary to use the symbol E rather than W.
In mechanics, the work done on an object is related to the forces acting on it by
- F is force
- Δd is the displacement of the object.
This is often summarized by saying that work is equal to the force acting on an object times its displacement (how far the object moves while the force acts on it). Note that only motion that is along the same axis as the force “counts”, however; a force in the same direction as motion produces positive work, and a force in an opposing direction of motion provides negative work, while motion perpendicular to the force yields zero work.
Differentiating by time gives that the instantaneous power is equal to the force times the object’s velocity v(t):
The average power is then
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