3.5 Power

Power measures the rate of energy transfer

Power is how quickly work is done or energy is transferred: P = W/t, measured in watts (W = J/s). A high-power machine transfers the same energy in less time. Power isn't about how much work is done overall — it's about how fast that work happens.

Power with force and velocity

Since W = F·d·cosθ, dividing by time gives P = F·v·cosθ, where v is velocity. For a force acting parallel to motion, this simplifies to P = Fv. This form is useful for analyzing engines, motors, or a person pushing an object at constant speed.

Average vs. instantaneous power

Average power uses total work divided by total time: P_avg = W_total/Δt. Instantaneous power is the power at one specific moment, often found using instantaneous velocity: P = Fv at that instant. Power can vary over time even if total work stays the same.

Key terms

Power

The rate at which work is done or energy is transferred; P = W/t.

Unit of power

Watt (W), equal to one joule per second (J/s).

Power in terms of force and velocity

P = Fv·cosθ; simplifies to P = Fv when force and velocity are parallel.

Average power

Total work done divided by total time elapsed: P_avg = W_total/Δt.

Instantaneous power

The power delivered at a specific moment in time, often calculated using instantaneous velocity: P = Fv.

Try an AP-style question

A machine does 600 J of work in 3 s. What is its power?

1. 1,800 W
2. 0.005 W
3. 200 W
4. 600 W