A high speed passenger test train travels from Columbia station to Penn station in exactly 8 hours. This distance traveled in miles from Columbia at any give time in hours is given by: s(t) = - 6t^3+72t^2.

a) How many miles has the train traveled 2 hours into the trip?

b)What is the distance in miles from Columbia station to Penn

c) What is the average speed of the train (AROC) between 2 and 5 hours

d) what is the velocity (IROC) of the train at exactly 2.5 hours into the trip.

e) what is the maximum velocity attained by the train? Please justify your answer

Thank you for all your help!!