Work says how much energy changed hands. Power says how quickly, and in engineering that is usually the number that sizes the motor. $P = \dfrac{W}{t}$, read aloud P equals W over t: $P$ is the power in watts, $W$ is the work or energy in joules, and $t$ is the time in seconds. One watt is one joule per second, and that is the entire definition — nothing else is hiding in it.

The second form is the same fact for something already moving: $P = Fv$, P equals F v, with $F$ the driving force in newtons and $v$ the speed in metres per second, the force acting along the motion. It falls straight out of the first — work is $Fd$, and $d/t$ is $v$. Use $P = W/t$ when you have a job and a clock; use $P = Fv$ when you have a machine running steadily. A conveyor at constant speed has no job that ever ends, so $P = Fv$ is the only one that answers.

Units guide, they do not confess. Run the check one way: J/s must come out as W, and N × m/s is N·m/s = J/s = W, so both forms survive. If your units refuse to land on watts, the rearrangement is wrong, no appeal — though units that do work out never prove you right.

Two nuggets for the trade. A kilowatt-hour is not a power at all — it is a kilowatt HELD for an hour, which is 3.6 million joules, and it is what the utility actually sells you. And one mechanical horsepower is 745.7 W, defined by Watt himself from what a dray horse could sustain, chosen so he could sell steam engines by the horse. The imperial twin of this lesson lives on that number.