Power is the rate at which work is done or energy is transferred in a unit of time. Power is increased if work is done faster or energy is transferred in less time.

The equation for power is P = W/t

- P stands for power (in watts)
- W stands for the amount of work done (in Joules) or energy expended (in Joules)
- t stands for the amount of time (in seconds)

In calculus terms, power is the derivative of work with respect to time.

If work is done faster, power is higher. If work is done slower, power is smaller.

Since work is force times displacement (W=F*d), and velocity is displacement over time (v=d/t), power equals force times velocity: P = F*v. More power is seen when the system is both strong in force and fast in velocity.

### Units of Power

Power is measured in energy (joules) divided by time. The SI unit of power is the watt (W) or joule per second (J/s). Power is a scalar quantity, it has no direction.

Horsepower is often used to describe the power delivered by a machine. Horsepower is a unit of power in the British system of measurement. It is the power required to lift 550 pounds by one foot in one second and is about 746 watts.

The watt is often seen in relation to light bulbs. In this power rating, it is the rate at which the bulb converts electrical energy into light and heat. A bulb with a higher wattage will use more electricity per unit of time.

If you know the power of a system, you can find the amount of work that will be produced, as W=Pt. If a bulb has a power rating of 50 watts, it will produce 50 joules per second. In an hour (3600 seconds) it will produce 180,000 joules.

### Work and Power

When you walk a mile, your motive force is displacing your body, which is measured as the work done.

When you run the same mile, you are doing the same amount of work but in less time. The runner has a higher power rating than the walker, putting out more watts. A car with 80 horsepower can produce faster acceleration than a car with 40 horsepower. In the end, both cars are going 60 miles per hour, but the 80-hp engine can reach that speed faster.

In the race between the tortoise and the hare, the hare had more power and accelerated faster, but the tortoise did the same work and covered the same distance in a much longer time. The tortoise showed less power.

### Average Power

When discussing power, people are usually referring to average power, P_{avg}. It is the amount of work done in a period of time (ΔW/Δt) or the amount of energy transferred in a period of time (ΔE/Δt).

### Instantaneous Power

What is the power at a specific time? When the unit of time approaches zero, calculus is needed to derive an answer, but it is approximated by force times speed.