Grade 12 Physics · The rate of doing work
Not how much — how fast
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Not how much — how fast

Everything so far totalled energy. Power asks how quickly it moved: P=WtP = \dfrac{W}{t}P equals W over t. PP is the power in watts, WW is the work or energy in joules, and tt is the time in seconds. One watt is one joule per second, and that is the entire definition. Carry a crate upstairs slowly or sprint it up: identical work, wildly different power.

There is a second road to the same watt. Substitute W=FdW = Fd and d/t=vd/t = v, and you get P=FvP = FvP equals F v, where FF is the driving force in newtons and vv the speed in m/s it is delivered at. Use P=W/tP = W/t when the story gives you a total job and a clock; use P=FvP = Fv when it gives you a force and a steady speed. Same relation, two doors.

The house trap of this lesson is the prefix. Motors, kettles and cars are quoted in kilowatts, and 1 kW=1000 W1\ \mathrm{kW} = 1000\ \mathrm{W}. An answer in kilowatts poured into a box marked watts is off by a factor of a thousand, which is not a rounding error — it is the difference between a hair dryer and a locomotive. Convert at the END, never inside the formula.