A cog system on the beginning segment of a roller coaster needs to get 25 occupied cars up a \(100-\mathrm{m}\) vertical rise over a time interval of \(60 \mathrm{~s}\). Each car experiences a gravitational force of \(5670 \mathrm{~N}\). The cars start at rest and end up moving at \(0.50 \mathrm{~m} / \mathrm{s}\).

(a) How much work is done by the cog system on the cars?

(b) What average power must the cog system supply?

(c) What would happen to the amount of work done by the cog system if the cars had to be lifted the same distance in \(30 \mathrm{~s}\) ?