Power
Power
- Two motors can do the same work; the better one does it faster. The quantity that measures “how fast” is .
The definition
Symbols
- = power (W)
- = work done (energy transferred) (J)
- = time taken (s)
- Power is the work done per unit time. The multiple-choice paper makes the exact words matter: “per unit time” is the accepted option, against near-copies like “in one second” (9702/12/O/N/24 Q15).
- The unit is the watt: . In base units that is kg m² s⁻³, a one-line homogeneity exercise from chapter 1 (9702/22/F/M/24 Q1(b)).
- Careful with the letter W: as a symbol it means work done, as a unit it means watt. Read the sentence around it.
Worked example
Smallest case: work over time
A motor does 300 J of work in 5.0 s. Find its power.
- .
Your turn— tap to reveal the worked answer (9702/21/M/J/25 Q3(a))
Define power. (9702/21/M/J/25 Q3(a))
Answer: power is the work done per unit time (equally accepted: the rate of energy transfer).
Using it: lifting and driving
Worked example
Exam version: a motor lifting a load
A motor lifts a load of weight 240 N through 150 m at constant speed in 1.0 minute. Show that the work done is 36 kJ, then find the useful output power. (9702/21/O/N/24 Q3(c))
- Constant speed, so the lifting force equals the weight: .
- Time in seconds: 60 s. .
Common mistake
Your turn— tap to reveal the worked answer (9702/22/M/J/25 Q1(b)(iii)-(iv))
A 920 kg car accelerates from rest to 17 m s⁻¹ in 5.8 s while doing 4.7 × 10⁴ J of work against resistive forces. Find the average output power, and state how the output power compares once the car holds a constant speed. (9702/22/M/J/25 Q1(b)(iii)-(iv))
- KE gained: .
- Total output = KE gained + resistive work: .
- .
- At constant speed the KE stops growing, so the output power is less: it only covers the resistive work.
Answer: 3.1 × 10⁴ W; less at constant speed.