power
Two movers each haul the same heavy crate up the same staircase. One does it in ten seconds, the other takes a full minute. They did the identical amount of work — same weight, same height — yet we rightly call the quick one more powerful. Power is the rate at which work is done, or equivalently the rate at which energy is transferred: not how much, but how fast.
The defining relationship is P = W / t — power equals work done divided by the time taken. If the work is done at a steady rate this is the whole story; for a force F pushing an object moving at speed v, it can be written instantly as P = F v. Power is measured in watts (W), where one watt is one joule per second, 1 W = 1 J/s. The old unit horsepower survives on car engines; one horsepower is about 746 W.
You meet power everywhere energy flows at a rate: a 60 W bulb converts 60 joules of electrical energy to light and heat every second, a car engine rated at 100 kW can do work fast, an athlete's power output is what tires them. Keep power and energy distinct: power is the flow rate, energy is the amount. A kilowatt-hour on your electricity bill is a unit of energy (one kilowatt sustained for one hour), not of power.
A 700 N person runs up a 4 m-high flight of stairs in 5 s. The work done against gravity is W = F d = 700 x 4 = 2800 J, so the power is P = W / t = 2800 / 5 = 560 W — roughly three quarters of a horsepower, sustained briefly.
Same climb done in half the time means double the power, even though the work is unchanged.
Power and energy are not the same thing. A 100 W and a 10 W heater can deliver the same energy if the weaker one runs ten times as long; the watt measures the rate of delivery, the joule (or kilowatt-hour) measures the total.