3. Suppose that equation 2(d) represents the position of a particle moving in a straight line where s is in meters and t is in secs. Find the velocity and acceleration of the particle at time t and determine when the object is moving left to right and right to left. When is the object at rest.

An automobile, traveling at a constant rate, starts at home at time t = 0 and ends up 10 hours later 200 miles from home. It than changes speed and continues for the next 10 hours ending up 300 miles from home. It takes another 10 hours for it to return home. On two separate set of axes, sketch graphs of the distance and velocity functions.

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

25. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the equation of the tangent line at the point (2, 1)? x? - 3y = 1 4х — Зу- 5 %3D 0 4x – 3y + 2 = 0 2х — 3у - 1 %3 0 4х — 3у + 5 %3 0 |