How does power measure the rate at which a machine does work?

In the context of technology and mechanics, power is defined as the time rate at which work is performed or energy is transferred. It measures how quickly a machine completes a task, allowing for the comparison of performance between different systems.12

Mathematically, power is expressed as the amount of work done ($W$) divided by the time interval ($t$) required to complete it:
$$P=\frac{W}{t}$$

For machines, power can also be calculated using the force applied and the speed of the object in the direction of that force, or, in the case of rotating shafts, as the product of torque and angular speed.1

Using power formulas is particularly useful for determining the efficiency of a machine, as it allows for the use of instantaneous values of load and motion rather than calculating average forces over a distance. Common units for measuring this rate include watts (joules per second) and horsepower.312