What happens to the power output if the time taken to do the same amount of work is doubled?

Power output is defined as the amount of work done over a specific period of time. Mathematically, power (P) can be expressed as:

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

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

If the time taken to do the same amount of work is doubled, the equation can be visualized as follows:

Let’s say the initial time taken to do work ( W ) is ( t ). Then the power output at that time is:

[ P_1 = \frac{W}{t} ]

If the time is doubled, the new time becomes ( 2t ). The power output now will be:

[ P_2 = \frac{W}{2t} ]

This shows that the new power output is half of the original power output:

[ P_2 = \frac{1}{2} P_1 ]

Thus, if the time taken to do the same work is doubled, the power output is halved. This relationship is critical because it highlights how power is inherently linked to both the work being done and the time taken to do it. Understanding this