Acceleration, velocity, position Suppose the acceleration of an object moving along a line is given by a(t) = -kv(t), where k is a positive constant and v is the object's velocity. Assume the initial velocity and position are given by v(0) = 10 and s(0) = 0, respectively. a. Use a(t) = v'(t) to find the velocity of the object as a func- tion of time. b. Use v(t) = s'(t) to find the position of the object as a function of time. dv ds - (by the Chain Rule) to find the dt ds dt dv c. Use the fact that- velocity as a function of position.

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v (for all times t). 4512 if 0 sts 3 405 if 3 26 15r3 if 0 sts 3 405 if 3 26