Power
Simple Explanation
Power measures how quickly work is done, or how quickly energy is transferred: P = W/t. Two machines can do exactly the same total amount of work, but the more powerful one does it faster.
Why Do We Need It?
Power ratings (on motors, engines, and appliances) tell you how quickly a device can do work — crucial for comparing machines that ultimately do the same job at different speeds.
Formula
Power
P = W / t
Power measures how quickly work is done, or how quickly energy is transferred — the same amount of work done faster means a greater power.
- P
- — power, in watts (W), where 1 W = 1 J/s
- W
- — work done (or energy transferred), in joules (J)
- t
- — time taken, in seconds (s)
When to use it: Whenever the rate at which work is done, or energy is transferred, needs to be found.
Worked Example
Find a crane's power
A crane does 24,000 J of work lifting a load in 8 s. Find its power.
Why Does This Work?
Dividing the total work done by the time it took gives exactly how much work is done, on average, every second — which is the definition of power, measured in watts (joules per second).
Real-Life Example
Comparing two car engines
Two cars can both eventually reach the same top speed, but one accelerates from 0 to 100 km/h much faster than the other.
The faster-accelerating car has a more powerful engine — it does the same amount of work (accelerating the car to that speed) in less time.
Practice
A motor does 15,000 J of work in 5 s. Find its power.
MediumA 400 W motor runs for 10 s. Find the total work done.
MediumCommon mistake
Confusing power with energy — power is the RATE of energy transfer (in watts), while work and energy are the total AMOUNT transferred (in joules); a low-power device left running for a long time can still transfer more total energy than a high-power device running briefly.
Quick Review
- P = W/t
- Power is measured in watts (W), where 1 W = 1 J/s.
- A more powerful machine does the same work in less time.