15. 16. 17. 18. 19. 20. 21. Suppose a particle moves 5 feet in t seconds according to the position function s(t) = t3 9:2 + 24:. a) Find the velocity at time t and after 1 second. b) When is the particle at rest? c) Find the acceleration at time t and after 1 second. Suppose a body moves 3 meters in a straight line in t seconds according to the position function s(t) = t3 6t2 + 9. a) Find the body's acceleration each time the velocity is zero. b) Find the body's speed each time the acceleration is zero. c) Find the total distance traveled by the body from t = 0 to t = 2. A rock is thrown vertically upward from the surface of the moon at a velocity of 24 m/s and reaches a height following the models = 24t Milt2 meters in t seconds. a) Find the rock's velocity and acceleration at time t. b) How long does it take the rock to reach its highest point? c) How high does the rock go? d) How long does it take the rock to reach half its maximum height? e) How long is the rock aloft? Find the most general antiderivative f(t) given f'(t) = 8% secttan t. Given f \"(t) = W cos it, answer the following. a) Find the most general antiderivative f (t). b) If f(0) = 2 and f (1) = 2, find the particular solution f (t). Find the particular solution f (x) given the initial condition. x+ c) f'(x) = flwhere f(1) = 5 d) f"(x) = 1231'2 + 6x 4 where f(0) = 4 and f(1) = 1 A particle has an acceleration given by a(t) = 2t + 1. Its initial velocity is 12(0) = -2 m/s and its initial displacement is 5(0) = 3 to. Find the position function s(t)