Power can be defined as the time rate of doing work or the amount of work done per second. That is the reason as to why the energy may be equal but if the rate of releasing the energy is different, then there will be a difference in the power. For example, when a kilogram of coal is burnt, it releases more energy than when a kilogram of Trinitrotoluene is detonated. But since the Trinitrotoluene reaction releases energy much faster as compared to the burning of the coal, the Trinitrotoluene is said to deliver far more power than coal.

Mathematically, power is the product of force exerted on an object and the velocity of the object, or product of the torque and the angular velocity when it comes to the circular motions.

Power can be represented by: P = F v, where the power, P is a scalar, and the S.I. units of power is Watt (W). One watt is equal to 1 Joule/sec which is equivalent to 1 kg m ^{2 }s ^{-3}. In British Engineering, the unit of power is horsepower where 1 horsepower (hp) = 746 W.

Power requires a physical change and a specified time in which the physical change occurs. This is the main difference from work, which is measured only in terms of a net change in the state of the physical universe. For instance the same amount of work is performed when carrying an object up a flight of stairs regardless of whether the person carrying it is walking or running. However, more power is needed for running since the work being performed is done in a shorter duration of time.

During our H2 Physics tuition classes, we have also encountered average power and instantaneous power.

**Average Power**: <P> = W / t = F d / t = F v, where t is the time interval within which work is done.

**Instantaneous Power**: Defined as the limiting value of the average power as the time interval *t* approaches/tends to zero.

If power P is constant, the amount of work done during a period of duration T is calculated as: W = P T

Practical Applications of Power

A practical application of power is the power developed at the output shaft of an electrical motor. This power is the product of the torque generated by the motor and the angular velocity of the output shaft.

Another practical application of power is the power developed by the car engine for the vehicle to move. This power is the product of the traction force of the wheels and the velocity of the vehicle.