In the definition of work , it is not clear, whether the same amount of work is done in own second or in one hour. The rate, at which work is done, is often of interest in practical applications.
Power is the measure of the rate at which work is being done.
If work ∆W is done in a time interval ∆t, then the average power Pav during the interval ∆t is defined as
If work is expressed as a function of time, the instantaneous power P at any instant is defined as
Where ∆W is the work done in short interval of time ∆t following the instant t.
For your information
Elastic spring force
Non conservative forces
Tension is a string
Propulsion force of a rocket
Propulsion force of a motor
Power and velocity
It is , sometimes, convenient to express power in terms of a constant force F acting on an object moving at constant velocity v. for example, when the propeller of a motor boat causes the water to exert a constant force F on the boat, it moves with a constant velocity v. the power delivered by the motor at any instant is, the, given by
The Si unit of power is watt, defined as one joule of work done in one second.
Sometimes, for example, in the electrical measurements, the unit of work is expressed as watt second. However, a commercial unit of electrical energy is kilowatt-hour.
One kilowatt hour is the work done in one hour by an agency whose power is one kilowatt.
Therefore, 1 kWh = 1000 W x 3600 s.
Or 1 kWh = 3.6 x 106 j = 3.6 M J
Example 4.2: A 70 kg man runs up a long flight of stairs in 4.0 s. the vertical height of the stairs is 4.5 m. calculate his power output in watts.
Solution: work done = mgh