Power

Power tells you how fast energy is transferred, and it is a Core topic every 0625 candidate must calculate. It is worth 2-4 quick marks on most papers, yet students throw them away by confusing power with energy. The distinction is the whole point.

What is power and how is it different from energy?

Power is the work done per unit time, or equally the energy transferred per unit time. In words: power = work done ÷ time taken. In symbols: $P = \dfrac{W}{t} = \dfrac{\Delta E}{t}$. The unit is the watt (W); 1 W means 1 joule transferred every second. Energy is an amount (J); power is a rate (J/s). A kettle and a phone charger can transfer the same energy, but the kettle does it far faster.

Quantity	Symbol	Unit
Power	$P$	W
Work done / energy transferred	$W$ (or $\Delta E$)	J
Time	$t$	s

Sensible reference values earn credit in explain questions: a phone charger runs near 10 W, a student climbing stairs develops roughly 300-500 W, and a kettle runs near 2000 W (2 kW). Quoting a realistic value shows the examiner you understand the scale.

How do power questions chain with work done?

Most Paper 3 and 4 power questions are the last step of a chain: find the force (often weight, $mg$), find the work done ($W = Fd$), then divide by time. Each step has its own mark, so a wrong early answer still earns later method marks through “error carried forward”, provided you show every line.

Worked Exam Question

A 54 kg student runs up a staircase of vertical height 5.0 m in 7.0 s. Use $g = 9.8\ \text{N/kg}$.

(a) Calculate the student’s weight. [1] (b) Calculate the work done against gravity. [2] (c) Calculate the student’s useful power output. [2]

Solution (a). $W = mg = 54 \times 9.8 = \textbf{529.2 N} \approx \textbf{530 N}$.

Solution (b). Equation: $\text{work} = \text{force} \times \text{distance}$. Substitute: $529.2 \times 5.0$. Answer: 2646 J ≈ 2600 J (2 s.f.).

Solution (c). Equation: $P = \dfrac{W}{t}$. Substitute: $P = 2646 \div 7.0$. Answer: $P = \textbf{378 W} \approx \textbf{380 W}$.

Mark scheme

• B1: 530 N (accept 529-530 N).
• M1: $W = Fd$ with their weight $\times\ 5.0$; A1: 2600 J.
• M1: $P = \dfrac{W}{t}$ with their energy $\div\ 7.0$; A1: 380 W. Error carried forward applies throughout.

Common Mistakes

• Dividing by the wrong time unit. A 2-minute time must become 120 s. Fix: convert to seconds before substituting; watts are joules per second.
• Using mass instead of weight. $54 \times 5.0 \div 7.0$ scores nothing. Fix: multiply mass by $g = 9.8\ \text{N/kg}$ first (some papers use 10, so read the question).
• Confusing W the unit with W the symbol for work. Fix: in your working, label work as “work” or $\Delta E$, and reserve W for watts in the answer.
• Using the slope length of the stairs. Work against gravity uses vertical height only. Fix: circle the vertical height in the question.
• Quoting too many figures. 378.0000 W invites a sig-fig penalty. Fix: give 2 or 3 significant figures, matching the data.

Exam Technique Tip

Before substituting, write the units next to every number: $2646\ \text{J} \div 7.0\ \text{s}$. If the units do not divide to give J/s, you have grabbed a wrong quantity. Catch it now, not after the paper. This ten-second check rescues more power marks than any amount of re-reading, because nearly every dropped mark here is a units slip, not a physics gap.

How This Is Examined

Power appears on all written papers, Core and Extended, with the same equation. Papers 1 and 2 (MCQ) test single-step $P = \dfrac{W}{t}$ and unit recognition. Papers 3 and 4 run the weight → work → power chain shown above; Extended may extend it into efficiency or electrical power ($P = IV$), which uses the same watt. The stair-climb experiment is a classic Paper 6 context: timing a climb with a stopwatch and discussing reaction-time uncertainty. Learn the chain once and it pays on every paper in the series.