Instantaneous power and units of power

Average power vs instantaneous power

Average power P = W/t gives an overall value over a time period t, but in reality a motor’s power varies at every instant (acceleration, braking, gradient, etc.). Instantaneous power describes the power at a specific moment. For a force F applied to an object moving at velocity v (with F parallel to v), it is expressed as:

P = F × v

This widely used formula allows us to relate force, velocity and power without involving work.

Units of power

The legal (SI) unit is the watt (W), where 1 W = 1 J/s. The following are also used:

• the kilowatt (kW): 1 kW = 1000 W
• the megawatt (MW): 1 MW = 10⁶ W
• the horsepower (ch), an older unit still used for engines: 1 ch ≈ 736 W

Device	Approximate power
Human being (sustained effort)	100 to 200 W
Scooter engine	5 to 10 kW
Car engine	50 to 150 kW
Power station	several hundred MW

Common pitfall

Be careful with conversions: a statement giving power in horsepower (ch) must be converted to watts before any calculations in the SI system. For example, 100 ch ≈ 73,600 W, or approximately 73.6 kW. Never mix units within the same calculation.