I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is
a(t) = Cos(Pi/30t)
the velocity is v(t) = 30Sin(Pi/30t) + C
and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct
So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which do I solve? I realize this is conceptual in some ways.
Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?