Group Members __________________________________________________________
Calculus I Clearing the Hill Project
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
0t
, then one model
for his acceleration in miles/minute2 is given by
5.1t
where t 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 (
0t
minutes) or after the finish time (
25.3t
minutes).
1. Find a formula for his velocity at time t, and one for the distance traveled at time
t. 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?
