A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 66 t, at which time the fuel is exhausted and it becomes a freely "falling" body. 15 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -23 ft/s in 5 s. The rocket then "floats" to the ground at that rate.

Determine the position function s and the velocity function v (for all times t).

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

Inner peace.. jk it's  a stable electron configuration