Power is the rate at which energy is transferred or converted. It answers the question: how fast is energy moving?
The unit of power is the Watt (W) — one Joule per second. Power is a scalar. Like energy, it has no direction.
The key insight is that power depends on both the amount of energy transferred and the time over which it's transferred. Two engines can do the same total work — but the one that does it faster is more powerful. Power is entirely about rate.
Average power is the total work done (or energy transferred) divided by the total time elapsed:
This is the form to use when you know the total work and the time interval over which it was done. It doesn't matter how the power varied during that time — you're averaging over the whole interval.
Same work, two different time intervals. Watch how power changes even though the total energy transferred is identical.
Energy transferred is identical — power is entirely about the rate. Double the time → half the power, same work done.
A motor lifts a 40 kg crate from the ground to a height of 6 m in 8 seconds. What is the average power output of the motor? (g = 10 m/s²)
Instantaneous power is the power delivered at a specific instant — when force and velocity are known at that moment:
This formula comes directly from combining P = W/Δt with W = Fd cosθ:
Set the force, speed, and angle between them. The graph shows constant power over time — the shaded area is the energy transferred in 5 seconds.
Drag angle to 90° — power drops to zero even though force and speed are both nonzero. Only the component of force along the direction of motion delivers power.
A car engine exerts a 3,000 N drive force while the car moves at 25 m/s on a flat road. What is the instantaneous power output of the engine?
On a Power vs. Time graph, the area under the curve equals the total energy transferred during that interval. This is directly analogous to the area under a velocity-time graph giving displacement, or a force-displacement graph giving work.
A machine's power output increases linearly from 0 W at t = 0 to 600 W at t = 10 s. How much total energy does it transfer in those 10 seconds?
The most common AP exam power problem combines power with the work-energy theorem from Lesson 3.4: given a power output and a resistive force, find the maximum constant speed, or given a speed, find how long it takes to do a given amount of work.
A car's engine delivers a constant 60 kW of power. Air resistance and friction provide a combined resistive force of 1,200 N. What is the car's maximum speed on a flat road?
Unit 3 complete. Progress Check 3 covers all five lessons — kinetic energy, work, potential energy, conservation, and power. Take it before moving to Unit 4.