Assignment 12 Study Questions - Calculus and Analytic Geometry I | MAC 2311, Assignments of Analytical Geometry and Calculus

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GROUP WORK I, SECTION 5.4 Clearing the Hill The late actor Jimmy Stewart drove a very old car. In fact, when he drove it up a certain hill on Route 66 (near the giant dinosaur) it would decelerate until it hit the top, and then accelerate down the hill until he could barely control it. It usually took him a full 3.25 minutes to go from the bottom of the hill on one side to the bottom of the hill on the other. When he told the story, he would usually specify that after driving one minute, his speed was 0.4 miles/minute. If we take the time he started up the hill as ¢ = 0, then one model for his acceleration in miles/minute? is given by ¢ — 1.5 where f is in minutes. Notice that this model is only valid for his time on the hill. We make no claim for its validity before the start of the climb (f = 0 minutes) or after the finish time (¢ = 3.25 minutes). I. Find a formula for his velocity at time ¢, and one for the distance traveled at time ¢. Include units in your answer. 2. What was his starting velocity in miles per hour? What was his final velocity in miles per hour? What was his minimum velocity in miles per hour? 3. When did he reach the top of the hill? 4. How far did he travel from start to finish?