If power is defined as work done over time, what would happen to the power if the time is increased while keeping the work constant?

Power is defined as the rate at which work is done, and the mathematical expression for power (P) can be given by the formula:

[ P = \frac{W}{t} ]

where ( W ) is the work done and ( t ) is the time taken to do that work.

If the amount of work done remains constant and the time duration over which this work is done is increased, the value of ( t ) in the equation increases. Since the work (W) is fixed, increasing ( t ) means that the fraction ( \frac{W}{t} ) will yield a smaller value. Consequently, the power output decreases.

This illustrates the inverse relationship between power and time when work remains constant: as time increases, power decreases. Therefore, the correct outcome when power is calculated under these conditions is that it would decrease.