P = E/t and P = Fv · Watts vs Kilowatts · Comparing Appliances
Think about two people climbing the same flight of stairs. If one person runs up and the other walks, they both transfer the same amount of gravitational potential energy. However, the runner does it in less time, so they have a greater power output.
Power is one of the most important ideas in physics because it helps us compare machines, engines, and electrical devices fairly — not just by how much energy they use, but by how quickly they use it.
| Symbol | Quantity | SI Unit |
|---|---|---|
| P | Power | watt (W) |
| E | Energy transferred | joule (J) |
| t | Time | second (s) |
The equation can be rearranged:
When a force moves an object at constant velocity, we can calculate power directly from the force and velocity — without needing to know the time or distance separately.
Here's where it comes from: Work done = Force × distance (W = Fd), and Power = Work done ÷ time (P = W/t). Since velocity v = distance ÷ time, combining these gives:
| Symbol | Quantity | SI Unit |
|---|---|---|
| P | Power | watt (W) |
| F | Force | newton (N) |
| v | Velocity | metre per second (m/s) |
This equation also rearranges:
Important: P = Fv only applies when velocity is constant (i.e. no acceleration). If the object is accelerating, more work is being done to increase kinetic energy as well.
Because power can range enormously — from tiny electronic circuits to huge power stations — we use different prefixes with the watt:
| Unit | Symbol | Equivalent in W | Example |
|---|---|---|---|
| Watt | W | 1 W | LED light bulb (~8 W) |
| Kilowatt | kW | 1000 W | Electric kettle (~3 kW) |
| Megawatt | MW | 1 000 000 W | Wind turbine (~2 MW) |
| Gigawatt | GW | 1 000 000 000 W | Nuclear power station (~3 GW) |
Conversion examples:
Every electrical appliance has a power rating in watts or kilowatts. This tells you how quickly it transfers energy when in use. A higher power rating means more energy used per second — which usually means higher running costs.
| Appliance | Typical Power Rating |
|---|---|
| Phone charger | 5–20 W |
| LED light bulb | 8–15 W |
| Laptop | 45–100 W |
| Television | 50–200 W |
| Microwave oven | 700–1200 W |
| Electric shower | 7000–10 500 W (7–10.5 kW) |
| Electric kettle | 2000–3000 W (2–3 kW) |
| Electric car (charging) | 7000–22 000 W (7–22 kW) |
To find the total energy transferred by an appliance, use E = P × t. Remember to convert time to seconds if you want energy in joules, or to hours if you want energy in kilowatt-hours (kWh) for electricity bills.
Comparing appliances: a microwave (900 W) heats food more efficiently than an oven (2000 W) because it transfers the energy directly to the food rather than heating the air inside. Even though it has a high power rating, it finishes in much less time — so total energy used is often lower.
Question 1: Which of the following is the correct unit for power?
Question 2: A lamp transfers 4500 J of energy in 90 seconds. Calculate the power of the lamp in watts.
Question 3: A motor has a power of 3 kW. What is this in watts?
Question 4: A car travels at a constant velocity of 20 m/s. The engine exerts a force of 2500 N. Calculate the power output of the engine in watts.
Question 5: A 500 W appliance runs for 5 minutes. How much energy does it transfer?
Challenge 1: A student lifts a 12 kg box from the floor to a shelf 1.8 m high in 3 seconds. Calculate the power exerted by the student. (g = 10 N/kg)
Challenge 2: A train engine has a power output of 4.5 MW and exerts a constant driving force of 180 000 N. Calculate the speed of the train in m/s and convert to km/h.
Challenge 3 (Extended): Appliance A has a power rating of 1200 W and is used for 45 minutes each day. Appliance B has a power rating of 800 W and is used for 75 minutes each day. (a) Which appliance transfers more energy each day? (b) How much more energy does it transfer? Give your answer in joules.
Challenge 4 (Higher tier): A rowing machine monitor shows that an athlete produces an average power of 250 W over a 20-minute workout. The athlete's muscles are only 25% efficient at converting chemical energy to mechanical work. Calculate the total chemical energy used by the athlete's muscles during the workout.