Just for fun and educational purposes, I wrote a Maxima script for sinusoidal accel profile and added it to
the paper.
The user enters max allowable acceleration and time-to-destination, and the script computes the equations for distance, speed, acceleration, and jerk versus time.. and plots them.
Attached is a sample graph generated with the script for max accel = 6.3 ft/sec
2 and time-to-distance = 3 seconds.
The vehicle goes from x=0, v=0, a=0, and jerk=13.2 at t=0
to x=9, v=0, a=0, and jerk=13.2 at t=3 seconds.