A force produces power P by doing work W in a time T. What power will be produced by a force that does six times as much work in half as much time?
A) 12P
B) 6P
C) P
D) P
E) P

Question

A force produces power P by doing work W in a time T. What power will be produced by a force that does six times as much work in half as much time?
A) 12P 
B) 6P 
C) P 
D) P 
E) P

Quizplus · Accepted Answer

Using the formula for power:

P = W/T

Let x be the force that produces power P.

Then, the force that does six times as much work in half as much time would be 6x and T/2, respectively.

Using the formula for power again:

P' = (6W)/(T/2)

P' = (6W)(2/T)

P' = 12W/T

P' = 12P

Therefore, the power produced by the force that does six times as much work in half as much time is 12P, or choice letter A.

A Force Produces Power P by Doing Work W in a Time