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Power

▶︎  Watch it animatedinteractive step-through · ~3 min · optional

Power is how fast energy moves, not how much: average power is the work over the time, P = W / t, instantaneous power is P = dW/dt, and a watt is a joule per second. Only the part of the force along the motion delivers power, P = F v cos θ, so a sideways force delivers nothing, and on a power-versus-time graph the area under the curve is the work.

POWER IS HOW FAST ENERGY MOVES: P = W / t P t 60 W 20 W midpoint of 60 and 20 = 40 W: the trap average power = W / t = 32 W area under the curve = work done P = F v cos θ · AREA UNDER P-t = WORK · CONSTANT P IS NOT CONSTANT v
An engine runs at 60 W for 3 s and then at 20 W for 7 s. The work is the area under the power-versus-time curve, 180 + 140 = 320 J, so the average power is 320 / 10 = 32 W: the flat blue line closing off the same area. The midpoint of the two values, 40 W, ignores that the low step lasts more than twice as long.
Power Explorer · Open the sandbox →

Power and energy get tangled three ways. Reading power as energy — watts as joules, or 'more power' as 'more total energy,' when a small power held longer can deliver more. Using the full force no matter the angle, when only F cos θ along the motion counts, so the normal force, or tension in circular motion, delivers zero power. And averaging the listed power values instead of dividing total work by total time, or reading constant power as constant speed when, for a force along the motion, the force actually falls as F = P / v.

The work

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Lesson
Power ›

How power measures how fast energy moves, average P = W / t and instantaneous P = dW/dt in watts, so the same work done faster is more power; why only the part of the force along the motion delivers power, P = F v cos θ, so a sideways force delivers nothing; and why average power is total work over total time, with the force falling as F = P / v when the power is held constant. Worked examples handle how-fast against how-much comparisons, power at an angle, and two-step average power read off a P-versus-t graph. Closes with a ten-scenario skill check on all three traps.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items on the main mistakes for Topic 3.5: treating power and energy as the same thing instead of a rate and an amount, using the full force no matter its angle to the motion, and averaging the power values off the list or reading constant power as constant speed. Take it cold to find what is shaky, or after the lesson to confirm it is not.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the mistakes you've missed and drill it on its own. The round is adaptive: two correct in a row clears it and you move on.

Take the diagnostic to identify your misconceptions
Diagnostic first