The equation for terminal velocity, vm, is:
Referring to the acceleration-time curve,
For any constant acceleration system, the distance traveled, s, in time, t, is related to the initial velocity, v0, and the
acceleration, a, by:
As the telescoping length is equal to s1 + s2 and the inner tube is equal to S3, and they are assumed to be of equal length
Simultaneous solution of equations (22) and (23), with simplification, results in:
which can be solved for t2-3 given the requirements of maximum acceleration, am, maximum rate of change of
acceleration, , and terminal velocity, vm. The time, t1-2, can be found from the revision of equation (22).