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There are two likely calculus applications of this problem. Both differential calculus and basic vector operations can be used to solve for power in a scenario, depending on how a problem is defined.
Power is the dot-product of a force vector and a velocity vector
and...
Power is a change in energy over time, or in differential terms:
dE/dt
If you were given a function that defined a system's energy with respect to time, you could derive it to find a function for that system's power output.
If you were given a force vector and a velocity vector and asked to find the total power applied to the system, you could take the dot product of the two vectors to find this.
Or, if you are not taking a calculus approach to it:
Average power is simply energy divided by time
The magnitude of power given a force and velocity can be found with the formula:
P=F*v*cos(theta)
Where F is the magnitude of the force
v is the magnitude of the velocity
theta is the angle between the two quantities.
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