Maximum Value of A?

Question

A car in a roller coaster moves along a track. In the time interval from t=0 to t=4 s, where A is a positive dimensionless constant.

v = sqrt[(A^2 + (3At^2 + 12At)^2]

The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding 20 m/s . Find the maximum value of A allowed by these regulations.

Answer 1

As A is positive v is increasing with t so the maximum speed is at t=4s
so
sqrt(A^2+(48A+48A)^2 <=20
so A =0.208