In physics, power is the rate at which work is performed or energy is converted^{[1]}^{[2]}
If ΔW is the amount of work performed during a period of time of duration Δt, the average power P_{avg} 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.
Contents
Units
The dimension of power is energy divided by time. The unit of power is the watt (W), which is equal to one joule per second. Other units of power include ergs per second (erg/s), horsepower (hp), metric horsepower (Pferdestärke (PS) or cheval vapeur, CV), and footpounds per minute. One horsepower is equivalent to 33,000 footpounds per minute, or the power required to lift 550 pounds by one foot in one second, and is equivalent to about 746 watts. Other units include dBm, a relative logarithmic measure with 1 milliwatt as reference; (food) calories per hour (often referred to as kilocalories per hour); Btu per hour (Btu/h); and tons of refrigeration (12,000 Btu/h).
Mechanical power
In mechanics, the work done on an object is related to the forces acting on it by
where
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):
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