-- Use power when you're dealing with an amount of energy
AND the time it took. Because ...
Power =
(amount of work done or energy moved)
divided by
(time to do the work or move the energy from one place to another).
-- Use an energy equation when you have to figure out an amount of energy.
It would come up in situations like this:
. . . . . how much work is done (work is energy)
. . . . . energy needed to melt some amount of ice
. . . . . energy needed to boil some amount of water
-- Use an efficiency equation when you're dealing with
. . . . . the amount of work, or energy, or power going in
. . . . . AND the amount of work, or energy, or power coming out.