POWER is the RATE at which energy is transferred or work is done.
Power tells us how QUICKLY energy is being used — not how much total energy.
EQUATIONS:
P = E ÷ t
P = W ÷ t
P = power (W)
E = energy transferred (J)
W = work done (J)
t = time (s)
UNIT: watt (W) = 1 joule per second
1 kilowatt (kW) = 1000 W
1 megawatt (MW) = 1,000,000 W
Rearrangements:
E = P × t
t = E ÷ P
Comparing Power
Two machines can do the SAME total work — but the more powerful one does it FASTER.
EXAMPLE:
Machine A: 1000 J in 10 s → P = 100 W
Machine B: 1000 J in 5 s → P = 200 W
Machine B is twice as powerful — same work, half the time.
Typical power values:
100 W lightbulb → 100 J/s transferred
2000 W kettle → 2000 J/s transferred
1000 W (≈1 kW) — elite sprinter sustained output
50–150 kW — typical car engine
POWER AND WORK DONE IN CLIMBING:
P = mgh ÷ t
This combines Ep = mgh with P = W/t — useful for stair/ramp problems.
Energy, Power and Time Calculations
ALWAYS convert time to SECONDS before calculating:
1 minute = 60 s
1 hour = 3600 s
EXAMPLE 1 — finding energy:
A 60 W bulb on for 5 minutes:
t = 5 × 60 = 300 s
E = 60 × 300 = 18,000 J
EXAMPLE 2 — finding power:
A motor transfers 36,000 J in 2 minutes:
t = 2 × 60 = 120 s
P = 36,000 ÷ 120 = 300 W
EXAMPLE 3 — stair climb:
60 kg person climbs 3 m in 4 seconds (g = 9.8):
W = mgh = 60 × 9.8 × 3 = 1764 J
P = 1764 ÷ 4 = 441 W
⚠️ Common Mistake
Time MUST be in SECONDS when using P = E/t with energy in joules. '5 minutes' = 300 s, NOT 5. Forgetting to convert is the most common mistake in power calculations.
📐 Variables
PPower (P) is measured in watts (W)
EEnergy transferred (E) is measured in joules (J)
WWork done (W) is measured in joules (J)
tTime (t) is measured in seconds (s)
📐 Key Equations
P = E ÷ t
P = W ÷ t
E = P × t
📌 Key Note
Power = rate of energy transfer. P = E/t = W/t. Unit: watt (W) = J/s. E = Pt. Always convert time to seconds. Higher power = same work done faster. P = mgh/t for climbing problems.
🎯 Matching Activity — Power Values
Match each scenario to the correct power value. — drag the symbols on the right to match the component names on the left.
100 W
Drop here
500 W
Drop here
200 W
Drop here
1 W
Drop here
Engine transfers 24,000 J in 2 minutes — P = 24,000 ÷ 120
1 joule transferred every second — the definition of 1 watt
Motor does 30,000 J of work in 1 minute — P = 30,000 ÷ 60
Device transfers 1000 J in 10 s — P = 1000 ÷ 10
⚽ FIFA Worked Examples
Power — Stair Climb
A 50 kg student climbs 4 m of stairs in 5 seconds. Calculate her power output. (g = 9.8 N/kg)
F
P = W ÷ t, where W = m × g × h
I
W = 50 × 9.8 × 4 = 1960 J; t = 5 s
F
P = 1960 ÷ 5
A
P = 392 W
🎯 Test Yourself
Question 1 of 2
1. A 2000 W heater is on for 3 minutes. How much energy does it transfer?
2. Two students both lift a 10 kg bag 5 m. Student A takes 10 s, B takes 20 s. How do their power outputs compare?
⭐ How Well Do You Understand This Topic?
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🤖 Ask Mr Badmus AI
Stuck? Just ask! 💬
I'll use FIFA for calculations and flag Higher/Triple content clearly.