← Back to Concepts

Definition of Power

Power in physics is the rate at which work is done or energy is transferred over time. It measures how quickly energy is used or produced. College Board LOVES to call power by its long name: the rate at which energy is done. If you see a question asking for the rate at which work is done, you are finding power.

Definition and Formula

\( P_{\text{avg}} = \frac{ΔW}{Δt} \)

Power \(P\) = Work done \(W\) divided by time interval \(t\)

Where:

\(P\) is the average power (watts, W)
\(W\) is work done (joules, J)
\(t\) is time taken (seconds, s)

Units of Power

The SI unit of power is the watt (W), which is equal to one joule per second (\(1\, \text{W} = 1\, \text{J/s}\)). Another common unit is the horsepower (hp), often used for engines (I wouldn't worry much about hp because it doesn't show up on the AP test):

1 horsepower = 746 watts

Alternate Formula Using Force and Velocity

\( P_{\text{instantaneous}} = \vec{F} \cdot \vec{v} = F v \cos{\theta} \)

Power = Force \(F\) applied × velocity \(v\) of the object in the direction of the force

This formula applies when a constant force causes an object to move at constant velocity.

Example Problem

Problem: A worker lifts a 50 kg box 3 meters high in 4 seconds. What is the power output?

Work done \(W = F \times d = m \times g \times h = 50 \times 9.8 \times 3 = 1470 \ \text{J}\)

Power \(P = \frac{W}{t} = \frac{1470}{4} = 367.5 \ \text{W}\)

Real-world Applications

Power ratings of engines and motors
Electrical appliances rated in watts
Measuring human power output in sports or work

Quick Tips

Power is about how fast work is done, not how much work.
Higher power means more energy transfer per unit time.
Time must be in seconds and work in joules for power in watts.

Check Your Understanding

A machine does 500 joules of work in 10 seconds. What is its power output?
A) 50 W
B) 5000 W
C) 5 W
D) 0.05 W
How many watts are in 2 horsepower?
A) 373 W
B) 1492 W
C) 746 W
D) 372 W
Which formula correctly calculates power?
A) \( P = \frac{W}{t} \)
B) \( P = W \times t \)
C) \( P = \frac{t}{W} \)
D) \( P = \frac{F}{v} \)
A boy applies a force of 100 N moves an object whos displacement is given by the function 5/4 * t³ - 5t. What is the power at t = 4?
A) 500 W
B) 20 W
C) 105 W
D) 95 W
Power is defined as:
A) The amount of work done
B) The rate at which work is done or energy is transferred
C) The force applied on an object
D) The time taken to do work