7.14:
Power
Power measures the rate at which work is done. The SI unit of power is watt, and it is defined as one joule of work done in one second.
Recall that work is the transfer of energy, therefore, power can be represented as the rate of transfer of energy. For example, a 100 watts light bulb shines brighter than a 50 watts light bulb because the energy emitted per second by the 100 watts bulb is double that of the 50 watts bulb.
Similarly, two weightlifters will do the same amount of work while lifting a weight to a specific height, but the one doing it in a shorter time will have more power output.
When the work done varies as a function of time, the power obtained by dividing the total work done by the total time taken is called the average power.
If the time intervals are reduced to find the power output at a particular point, it is called instantaneous power. It is equal to the average power when the power is constant over a time interval.
7.14:
Power
The concept of work involves force and displacement; meanwhile, the work-energy theorem relates the net work done on a body to the difference in its kinetic energy, calculated between two points on its trajectory. While none of these quantities or relations involves time explicitly, we know that the time available to accomplish work is often just as important as the amount of work itself. For example, sprinters in a race may have achieved the same velocity at the finish, therefore, accomplishing the same amount of work, but the winner of the race did it in the least amount of time.
We can express the relationship between work done and the time taken to do it by introducing the concept of power. Since work can vary as a function of time, we first define average power as the work done during a time interval, divided by the interval. Work and energy are measured in units of joules, so power is measured in joules per second, which has the SI name watts, W: 1 J/s = 1 W. Another common unit for expressing the power capability of everyday devices is horsepower: 1 hp = 746 W.
This text is adapted from Openstax, University Physics Volume 1, Section 7.4: Power.