JEE/NEET Physics · Work, Energy & Power series · Part 5 of 8 · All parts →
- Power = work done per second (P = W/t) — the speed of energy transfer
- One watt = one joule per second; your household runs on kilowatts
- The two workhorse forms: P = Fv (force × speed) and P = mgh/t (lifting)
- Efficiency = useful output ÷ total input — nothing real is 100%
- Same energy in less time = more power
Two students carry the same 20 kg load up the same stairs — identical work. One takes 1 minute, the other takes 10 seconds. Same work, wildly different POWER. Power is the speed of doing work — and it’s what engines, motors and athletes are actually rated in. Part 5 of the Work, Energy & Power series.
- Power, simply
- What each letter means
- The two workhorse formulas
- Efficiency: nothing is 100%
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Power, Simply
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| P | power | watts (W) = joules/second |
| W | work (or energy) delivered | joules |
| t | time taken | seconds |
Feel the numbers: a phone charger ~20 W, a ceiling fan ~75 W, a microwave ~1,000 W, a car at highway pace ~20,000 W, a cricket ball’s throw delivered in 0.1 s ~ 1,000 W momentarily. Horsepower (car specs) = 746 W.
The Two Workhorse Formulas
P = Fv is why cars struggle uphill: at fixed engine power, more needed force (climbing) forces less speed. It’s also why you slow down when cycling into a headwind — same legs (power), more force needed, so speed must drop.
Efficiency: Nothing Is 100%
A car engine is ~25-35% efficient (most fuel energy becomes heat); an LED bulb ~40-50% (vs an old filament bulb’s ~5% to light); an electric motor ~85-95%. Efficiency questions are pure percentage bookkeeping — keep the ‘useful’ clear.
Solved Examples
Work: mgh = 60 × 10 × 4 = 2,400 J. Power: 2,400/10 = 240 W — about three fans’ worth, sustained by legs. ✔
Answer: 240 W
P = Fv: F = 40,000/20 = 2,000 N.
Check the physics: steady speed means this force exactly balances air + road resistance. Need more force (uphill)? Speed must fall — power is fixed. ✔
Answer: 2,000 N
Useful output: mgh = 10⁷ J; useful power = 10⁷/500 = 20 kW.
Efficiency 80%: input = 20/0.8 = 25 kW.
The missing 5 kW = motor heat — that’s what the 80% meant. ✔
Answer: 25 kW drawn from the grid
- Confusing energy and power. A 100 W bulb used for 10 hours consumes 1,000 Wh = 1 unit of electricity — power × TIME is energy; bills charge for energy.
- Forgetting P = Fv needs STEADY speed (or use it as average force × average speed — be consistent).
- Efficiency above 100%. Impossible — if your answer says 120%, you divided the wrong way. Output ÷ input, never the reverse.
- Mixing units. horsepower × 746 = watts; hours × 3,600 = seconds — convert before dividing.
This Physics in Your Daily Life
- Your electricity meter counts kilowatt-HOURS: power (kW) × time (hours) — the unit on every bill is literally this card.
- Fan/AC star ratings are efficiency labels: same cooling, fewer watts — the same physics saving you money.
- Cars advertise horsepower (1 hp = 746 W) — the rate at which the engine can deliver energy; ‘torque × rpm’ from our Rotational series is the same number in disguise.
- Cycling into a headwind: your legs have fixed power; more drag force → less speed — P = Fv lived experience.
- Cricket fast bowlers: ~150 J into a ball over ~0.1 s of delivery ≈ 1,500 W — sprinter-level power from a standing run-up.
Practice set (answers hidden — try first)
(NEET-level) A 50 kg person climbs 5 m in 25 s. Power (g = 10):
(JEE Main-level) An engine of 25 kW pushes a car at 10 m/s. Driving force:
(NEET-level) A 2 kW heater runs 3 hours. Energy consumed:
(JEE Main-level) A motor draws 5 kW to deliver 4 kW useful. Efficiency:
(Concept) At fixed engine power, climbing a hill, the car’s speed:
- 🧠 Chant: ‘work is how much, power is how fast’.
- 🧠 P = Fv: ‘fixed engine, hills eat speed’.
- 🧠 Bill math: ‘watts × hours = the unit on the meter’.
- 🏠 Daily: every appliance sticker in your kitchen is this card in print.
- 🏠 Daily: headwind cycling is P = Fv you can feel in your thighs.
- 🔁 P = W/t (watts); P = Fv; P = mgh/t for lifting
- 🔁 efficiency < 100%, always
- 🔁 1 hp = 746 W; 1 kWh = 3.6 MJ
- P = W/t, watts = joules/second
- P = Fv — the engine formula; more force = less speed at fixed power
- lifting: P = mgh/t
- efficiency = useful out ÷ total in — always < 100%
- 1 hp = 746 W; 1 kWh = 3.6 MJ (your bill’s unit)
Quick revision
- Power = work done per second (P = W/t) — the speed of energy transfer
- One watt = one joule per second; your household runs on kilowatts
- The two workhorse forms: P = Fv (force × speed) and P = mgh/t (lifting)
- Efficiency = useful output ÷ total input — nothing real is 100%
- Same energy in less time = more power
- The two workhorse formulas
- 1Work Done: When a Force Actually Achieves Something
- 2Kinetic Energy and the Work-Energy Theorem: The Great Shortcut
- 3Potential Energy: Stored Work, Ready to Strike
- 4Conservation of Energy: The Universe’s Perfect Bookkeeping
- 5Power and Efficiency: How FAST You Can Do the Work
- 6Collisions: The Great Sorting — What Survives, What Dies
- 7Springs and Vertical Circles: Energy in Two Classic Stages
- 8The Finale: Energy in the Real World, and the Complete Formula Card
Have a doubt on this topic?
