A high-speed bullet train accelerates and decelerates at the rate of 3 ft/s2. Its maximum cruising speed is 90 mi/h. (Give your answers correct to one decimal place.)

$\displaystyle a(t) = 3$

$\displaystyle v(t) = 3x+C$ x<$\displaystyle \frac{90-C}{3}$

$\displaystyle s(t) = \frac{3x^2}{2}+Cx+D$

(a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?

(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance it can travel under these conditions?

(c) Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart.

I was trying to solve for C originally, at t=0, v = 0, which gave me C = 0, but doing the same thing for distance gives me that D = 0 too. This seems...wrong.

I'm too tempted to figure out how to solve these using equations of motion, so I'm drawing a blank on what to do for these above. Any hints would be appreciated.