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?

OK. Fasten your seat belt. It may be a boompy ride.

Let's say that ' W ' is a certain amount of work, and

' T ' is a certain amount of time.

So when you calculate W/T, you get ' P ' ... a certain amount of power.

NOW ... we want to know how much power will be required

in order to do 6W of work in 0.5T.

Fine! THAT power will be

(6W/0.5T)

= (6/0.5) (W/T)

= (12) (W/T).

But (W/T) is the original amount of power ... ' P '.

So the new scenario requires 12 times as much power, or (12 P).