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Learn7367Paper 3 · Mechanics optionWork, energy and powerPower
Work, energy and power · Subtopic 4 of 4

Power

Power is how fast work is done: joules per second, or watts. For a vehicle, P=FvP=Fv, so the same engine pushes hard at low speed and gently at high speed, which is why every car has a top speed.

Cambridge 9709 Paper 4Edexcel YMA01 WME02Edexcel 9FM0 OptionAQA 7367 Paper 3≈ 35 minRevision 6 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Define power as the rate of doing work, in watts.
  • Use P=FvP=Fv to find the driving force at a given speed.
  • Find a vehicle's maximum speed, where driving force equals total resistance.
  • Find accelerations and speeds for vehicles on hills.
Pause and think

A car's engine works at a constant 3030 kW. At 5 m s−15\ \text{m s}^{-1} and at 30 m s−130\ \text{m s}^{-1}, is the driving force the same?

Section 2 of 14

Core idea

Start hereWhy cars have a top speed

A car's engine has a fixed maximum power: energy per second. At low speed that power gives a big push; at high speed the same power gives a small push. Eventually the push only just matches air resistance and the car can go no faster.

The big idea

Power P=WtP=\frac Wt (watts). For a vehicle, P=FvP=Fv with FF the driving force. Top speed: driving force = resistance.

1. P = Fv

P=FvP=Fv
  1. P=Wt=FdtP=\frac Wt=\frac{Fd}t
    Definitions.
  2. =F⋅dt=Fv=F\cdot\frac dt=Fv
    Distance per time.
A car with power 30 kW against 1500 N resistance
5101520253035401000200030004000500060000speed v (m/s)force (N)driving force = P/vresistancemax speed 20 m/s
At low speed the driving force is bigger than the resistance, so the car accelerates. As speed rises, P/vP/v falls until it equals the resistance: v=300001500=20v=\dfrac{30000}{1500}=20 m/s.
Worked example30 kW car, 1500 N resistance, 1200 kg

Top speed, and acceleration at 10 m/s.

Goal
Values.
Strategy
F=PvF=\frac Pv.
  1. 30000v=1500⇒v=20\frac{30000}v=1500\Rightarrow v=20
    Top speed: FF = resistance.
  2. F=3000 at 10 m/sF=3000\text{ at }10\text{ m/s}
    Pv\frac Pv.
  3. a=3000−15001200=1.25a=\tfrac{3000-1500}{1200}=1.25
    F=maF=ma.
Answer2020 m/s; 1.251.25 m s−2^{-2}.
✓ CheckAcceleration falls as speed rises ✓.
Worked exampleUphill

Same car up a slope with sin⁡α=120\sin\alpha=\frac1{20}. Top speed?

Goal
vv.
Strategy
Add mgsin⁡αmg\sin\alpha to resistance.
  1. 12000×120=60012000\times\tfrac1{20}=600
    Weight component.
  2. v=300002100=14.3v=\tfrac{30000}{2100}=14.3
    Balance.
Answer14.314.3 m/s.
✓ CheckLower than on the flat ✓.
Pause and think

Power for 25 m/s against 800 N?

Summary

  • P=W/t=FvP=W/t=Fv.
  • Top speed: F=F= resistance.
Key words
Watt
Joule per second.
HistoryHorsepower. To sell his steam engines in the 1780s, James Watt needed to compare them with the horses they would replace. He estimated that a mill horse could do 33 00033\,000 foot-pounds of work per minute, about 746746 W, and called it one horsepower. The SI unit of power, the watt, was later named after him.
Fun factHow powerful are you? A fit adult can sustain about 100100 W for hours, and a top cyclist in the Tour de France around 400400 W for an hour. Running up stairs briefly, you might manage 600600 W or more. A family car engine produces around 75 00075\,000 W, the work of a hundred people.
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