Power

Power measures the rate of energy transfer or transformation. The same amount of energy can be delivered slowly or quickly.

The learner question

How can two devices transfer the same energy but behave very differently?

Power adds time to the energy ledger. A high-power process moves the same energy through the system boundary in less time.

Core relationship
P=ΔEΔtP = \frac{\Delta E}{\Delta t}

1 watt = 1 joule per second.

Transfer-rate lab
energy crossing boundary
energy
120 J
time
4.0 s
power
30.0 W
Energy transferred120 J
Transfer time4.0 s
Same energy, half the time
60.0 W

Power doubles because the transfer rate doubles.

Double the energy, same time
60.0 W

Power also doubles because twice as much energy crosses in the same interval.

Mechanical connection

When a force acts along an object's velocity, instantaneous mechanical power can also be written P=FvP = Fv.

Transfer check

A motor does the same work but takes twice as long. What happens to its average power?