The big idea: Power is how fast energy is transferred — the energy moved each second.
Same job done quicker = more power.
Unit: the watt (W), which is just 1 joule per second (J s⁻¹).
Spot it — P = Fv at a steady speed: When something moves at a constant speed, the driving force balances the resistive (drag) force.
So the power is P = Fv, where F is the resistive force. Faster cruise ⇒ more power needed.
Power has two given forms in the data booklet. Use P = ΔW/Δt when you know the energy transferred and the time; use P = Fv when a force moves at a steady speed (for example a vehicle cruising against drag).
- power — energy transferred per second (W, watts = J s⁻¹)
- work done / energy transferred (J, joules)
- time taken (s)
- the force (N) — at constant speed, equal in size to the resistive force
- speed in the direction of the force (m s⁻¹)
Average vs instantaneous power: Average power = total energy ÷ total time (use ΔW/Δt over the whole interval).
Instantaneous power = the power right now (use Fv with the speed at that moment).
Define: 'instantaneous' means at one instant, not averaged over time.
Worked example — average power
A motor lifts a load, transferring 6000 J of energy in 4.0 s. Find its average power output.
Solution
- Start with the given formula (energy and time, so use ΔW/Δt):
- Put in the numbers (ΔW = 6000 J, Δt = 4.0 s):
- Work it out — keep the unit:
Final answer
average power = 1500 W = 1.5 kW.
Worked example — power against drag at constant speed
A car cruises at a steady 25 m s⁻¹ against a total resistive force of 480 N. Find the power its engine delivers.
Solution
- At constant speed the driving force equals the resistive force, so use the given P = Fv:
- Put in the numbers (F = 480 N, v = 25 m s⁻¹):
- Work it out — keep the unit:
Final answer
power = 12 000 W = 12 kW.
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How this is tested: Power and efficiency appear across both papers.
- Paper 1A: a quick average power (energy ÷ time), e.g. a spring releasing its stored energy. - Paper 2: the classic 'determine the drag constant from power and speed at constant velocity' — then state its SI unit — and average power delivered to an object that started from rest.
Classic trap: at constant speed the engine force equals the resistive force, so P = Fv lets you find that force (or a drag constant) from the power and the speed.
Drag constant from power & speed: For many objects the drag force grows with speed as F = cv, where c is the drag constant.
At constant speed P = Fv = cv × v = cv², so c = P ÷ v².
Its unit comes from the units: W ÷ (m s⁻¹)² = kg s⁻¹ (work it out from N = kg m s⁻²).
IB-style question — (a) the drag constant
A boat moves at a steady 5.0 m s⁻¹. Its engine delivers 750 W, and the drag force on it is given by F = cv. Determine the drag constant c.
Solution
- At constant speed the engine force equals the drag, so start with the given P = Fv:
- Put in F = cv, so P = cv × v = cv²:
- Rearrange for c and put in the numbers (P = 750, v = 5.0):
- Work it out:
Final answer
drag constant c = 30 (in SI units of kg s⁻¹ — see part (b)).
IB-style question — (b) its SI unit
State the fundamental SI unit of the drag constant c.
Solution
- From c = P ÷ v², put in the units (P in W, v in m s⁻¹):
- Write the watt in base units (1 W = 1 J s⁻¹ = 1 kg m² s⁻³):
- Cancel — the m² cancels completely and s⁻³ ÷ s⁻² leaves s⁻¹:
Final answer
the SI unit of c is kg s⁻¹ (kilograms per second).