Average Power:

The average power is defined as the work done divided by the time required; its units are J/s, for which the name watts (W) is given. The horsepower is a common unit in the U.S. Customary System,

(Work is measured in ft lbs in this system.)

Comment about units: We usually pay for electrical "power" in cents per kilowatt-hr (kwh). Since a watt is J/s and a kilowatt is 1000 times this, multiplying by hours means that the kwh is really a unit of energy (Joules divided by 1000 and multiplied by 3600). We pay for energy consumed, not power!

Instantaneous Power:

The instantaneous power is given by

Kinetic Energy at High Speeds:

We've been using the classical (non-relativistic) expression for kinetic energy:

This is valid only for speeds that are low compared to that of light (c = 3 x 10⁸ m/s). The relativistic form is:

To see how one can show that this equation reduces to the classical expression for low speeds, check this link...

Example 1: The donkey and the well

Example 2: An accelerating rocket

Example 3: Classical vs Relativistic Kinetic Energy