Power

What power means in physics, how to calculate it, and the difference between energy and power.

What is Power?

Power is how quickly energy is transferred or work is done.

Power

P = \dfrac{W}{t}

P = power in W, W = work/energy in J, t = time in s

Work done

W = F \cdot d

force × distance, measured in Joules (J)

Units

Quantity	Unit	Symbol
Power	Watt	W
Energy / Work	Joule	J
Time	Second	s

1 kilowatt (kW) = 1000 W

A motor lifts a 200 N load through 3 m in 6 s.

Work done: $W = 200 \times 3 = 600 \text{ J}$

Power: $P = \dfrac{600}{6} = 100 \text{ W}$

A light bulb uses 60 W for 5 minutes. How much energy does it use?

$t = 5 \times 60 = 300 \text{ s}$

$E = P \times t = 60 \times 300 = 18\,000 \text{ J} = 18 \text{ kJ}$

Note

A 1 W device transfers 1 J of energy every second.

Real world: Cyclist climbing a hill

A cyclist pedals up a hill, applying an average forward force of 80 N while moving at a constant 5 m/s.

Power output: $P = F \times v = 80 \times 5 = 400 \text{ W}$

That is a realistic sustained effort for a fit amateur cyclist — elite riders can sustain over 400 W for hours.

Real world: Electric lift in a warehouse

A warehouse lift raises a 600 kg pallet by 4 m in 8 s.

Work done: $W = mgh = 600 \times 10 \times 4 = 24{,}000 \text{ J}$

Power: $P = \dfrac{24000}{8} = 3{,}000 \text{ W} = 3 \text{ kW}$

A typical electric forklift motor is rated between 2 kW and 15 kW.

Real world: Car engine on a motorway

A 1,200 kg car cruises at 30 m/s against an air-resistance force of 600 N.

Power needed just to maintain speed: $P = F \times v = 600 \times 30 = 18{,}000 \text{ W} = 18 \text{ kW}$

A typical petrol engine produces 70–150 kW total — most of that is available for acceleration, heating, and other losses.

Tip

Where do you see this in real life? Every appliance, vehicle, or athlete has a power rating. A faster lift, a more powerful engine, or a fitter cyclist all do the same work — they just do it in less time.

Practice Problems

A pump transfers 5,000 J of energy in 25 s. What is its power?

Show answer

P = 5000 ÷ 25 = 200 W.

Which is more powerful: a device that does 400 J in 4 s, or one that does 600 J in 8 s?

Show answer

Device 1: 400/4 = 100 W. Device 2: 600/8 = 75 W. Device 1 is more powerful.