Work and Time
Elementary School
Definition
The relationship between the work done and the time taken to do it, which defines power. Doing the same work in less time requires more power, so power measures how quickly energy is transferred or transformed.
Worked examples
\(P = \frac{W}{t}\)
Power equals work divided by time — the same work done faster means higher power.
Lifting 50 kg by 2 m in 5 s: \(W = mgh = 50 \times 10 \times 2 = 1000\,\)J\(\); \(P = \frac{1000}{5} = 200\,\)W\(\)
Doing 1000 J of work in 5 seconds requires 200 watts of power.
Doing the same 1000 J in 2 s: \(P = \frac{1000}{2} = 500\,\)W\(\)
Less time for the same work means more power is needed.
Common mistakes
- \(P = W \times t\) → \(P = \frac{W}{t}\) Power is work divided by time, not multiplied — more time for the same work means less power.
- Power and work are the same thing → Power is the rate of doing work Work measures total energy transferred; power measures how quickly that energy is transferred.
- If time doubles, power doubles → If time doubles (for the same work), power is halved Power is inversely proportional to time when work is constant.
Where you'll use it next
You'll use the work-time-power relationship when studying mechanical advantage, engines and motors, electrical circuits, and energy efficiency in physics and engineering courses.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026