Work can be done very quickly rather slowly; there can be difference rates at which work is done.

Power is the rate at which work is done or the work/time ratio.
The equation for rate of doing work or power is:

$$\mathrm{power}=\frac{\mathrm{work}}{\mathrm{time}}$$
or

$$P=\frac{W}{t}$$
The SI unit of power is the Watt.
As implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time, that is, joule/second or J/s.

## An Alternate Formula for Power

Given that:

$$P=\frac{W}{t}$$
Work done is:

$$W=Fs$$
where $F$ is the force displacing an object by $s$.

Combining the equations for work with that for power

$$P=\frac{Fs}{t}$$
Since the expression for velocity is

$$v=\frac{s}{t}$$
The expression for power can be rewritten as

$$P=Fv$$
This new equation for power shows that a powerful machines are both strong (i.e., large force) and/or fast (i.e., high velocity).

## An Equation for Electrical Power

$P=IV$

Machines do work on objects and will have a power rating. This power rating gives the rate the machine can do work on a process.
A car engine is an example of a machine that is given a power rating.
The power rating relates to how rapidly the car can accelerate the car.
Suppose that a 40-horsepower engine could accelerate the car from 0 mi/hr to 60 mi/hr in 16 seconds.
If this were the case, then a car with four times the horsepower could do the same amount of work in one-fourth the time.
That is, a 160-horsepower engine could accelerate the same car from 0 mi/hr to 60 mi/hr in 4 seconds.
The point is that for the same amount of work, power and time are inversely proportional.
The power equation suggests that a more powerful engine can do the same amount of work in less time.
A person is also a machine that has a power rating.Some people are more power-full than others.
That is, some people are capable of doing the same amount of work in less time or more work in the same amount of time.
A common physics lab involves quickly climbing a flight of stairs and using mass, height and time information to determine a student's personal power.
Despite the diagonal motion along the staircase,
it is often assumed that the horizontal motion is constant and all the force from the steps is used to elevate the student upward at a constant speed.
Thus, the weight of the student is equal to the force that does the work on the student and the height of the staircase is the upward displacement.
Suppose that Ben Pumpiniron elevates his 80-kg body up the 2.0-meter stairwell in 1.8 seconds.
If this were the case, then we could calculate Ben's power rating.
It can be assumed that Ben must apply an 800-Newton downward force upon the stairs to elevate his body.
By so doing, the stairs would push upward on Ben's body with just enough force to lift his body up the stairs.
It can also be assumed that the angle between the force of the stairs on Ben and Ben's displacement is 0 degrees.
With these two approximations, Ben's power rating could be determined as shown below.
Ben's power rating is 871 Watts. He is quite a horse.