Physics
posted by Brent .
In a city with an airpollution problem, a bus has no combustion engine. It runs on energy drawn from a large, rapidly rotating flywheel under the floor of the bus. The flywheel is spun up to its maximum rotation rate of 5150 rev/min by an electric motor at the bus terminal. Every time the bus speeds up, the flywheel slows down slightly. The bus is equipped with regenerative braking so that the flywheel can speed up when the bus slows down. The flywheel is a uniform solid cylinder with mass 1600 kg and radius 0.650 m. The bus body does work against air resistance and rolling resistance at the average rate of 18.0 hp as it travels with an average speed of 40.0 km/h. How far can the bus travel before the flywheel has to be spun up to speed again?

It will travel until the initial kinetic energy of the flywheel equals the work that has to be done to keep the bus moving for a time t.
(1/2)Iw^2 = (Power)*time
Power = 18.0 hp = 13,428 J/second
You don't need to know or use the average speed.
Sngular velocity w = 5150 rev/min*(2 pi rad/rev)/(60 s/min)
= 539.3 rad/s
I = (1/2)M*R^2 = 338 kg*m^2
Solve for time