Power Delivered
P = F·v — see instantaneous and average power grow as velocity increases.
Key Notes
Power P is the rate of doing work or transferring energy: P = dW/dt.
Units: watt (W) = J/s. 1 kW = 1000 J/s.
Average power: P_avg = W/Δt. Instantaneous: P = F·v (for constant or varying force).
Power required to move at constant velocity against friction: P = F_friction × v.
Acceleration phase: P keeps increasing if you maintain F = F_friction + ma.
Power output of a car engine: V_max occurs when all engine power goes against drag — P = F_drag × V_max.
Vehicles, machines, appliances all rated by power. Human body produces ~75 W steady; up to ~1500 W in short bursts.
Electrical: P = VI = I²R = V²/R. Mechanical: P = F·v.
Formulas
Average power
Energy / time interval.
Instantaneous power
Force × velocity (dot product).
Mechanical power at constant velocity
Most useful form in vehicle problems.
Electrical power
DC and instantaneous AC.
Important Points
Power tells you HOW FAST work is done — not HOW MUCH.
1 horsepower = 746 W. Car engines: 100-500 hp = 75-375 kW.
Doubling speed at constant force ⇒ doubling power demand. Aerodynamic drag (F ∝ v²) ⇒ power ∝ v³.
Climbing stairs at jog vs walk: same work done (mgh), but jogging takes less time ⇒ higher P.
Power-to-weight ratio is critical for sports cars, aircraft — measures acceleration capability.
Energy = power × time. A 100 W bulb on for 10 hours = 1 kWh = 3.6 MJ.
Power Delivered notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.