The preliminary design for a rapid-transit system calls for the train velocity to vary w...

The preliminary design for a rapid-transit system calls for the train velocity to vary with time as shown in the plot as the train runs the two miles between stations A and B. The slopes of the cubic transition curves (which are of form a + bt + ct² +dt³) are zero at the end points. Determine the total run time t between the stations and the maximum acceleration.