Power is the rate at which work is done.

P = dW/dt

The MKS unit for power is the watt (W).

1 W = 1 J/s

When the force is constant, and with work given by W = F • d , the power equation becomes

P = F • v

Note that 1 hp = 746 W

An interesting calculation is the average power output of a human being. This can be determined from the amount of energy we consume in a day in the way of food. Most of us take in something like 2500 "calories" in a day, although what we call calories is really a kilocalorie. Use this as our energy output per day.

Take the 2.5 x 10⁶ cal and convert to joules, using the conversion factor:

1 cal = 4.186 J

This gives roughly 1 x 10⁷ J. Figuring out our average power output, we simply divide the energy by the number of seconds in a day, 86400, which gives a bit more than 100 W. In other words, on the average, we're just a little brighter than your average light bulb.

A car with a mass of 900 kg climbs a 20 degree incline at a steady speed of 60 km/hr. If the total resistive forces acting on the car add to 500 N, what is the power output of the car in watts? In horsepower?

As usual, draw a free-body diagram.

Using a coordinate system with +x up the slope and +y perpendicular to the slope, the gravitational force is the only force that needs to be split into components.
mg sin(20) acts down the slope
mg cos(20) acts into the slope

F_r represents the resistive forces.

The power output by the car's engine goes into the force directed up the slope. This force is actually static friction exerted on the drive wheels by the road - the road exerts this force F because the engine causes the drive wheels to rotate. With no friction they would spin on the road - friction opposes this tendency.

The velocity is constant, so the forces must balance. Applying Newton's second law in the x-direction gives:

F - F_r- mg sin(20) = 0

The force up the slope is then

F = F_r + mg sin(20) = 500 + 3017 = 3517 N

Converting the car's speed to m/s gives 16.67 m/s. The power output can then be found from

P = Fv = (3517) (16.67) = 58620 W.

This can be converted to horsepower, using 1 hp = 746 W. This gives a power output of 78.6 hp.

Most cars have engines with maximum power outputs of about 100 hp, so this is a reasonable value.