MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A car travels along a straight track. Its velocity v(t) (in meters per second) as a function of time t (in seconds) is described by the following piecewise graph.
• v(t)=0 for t≤0.
• v(t)=5 for 0<t<4.
• On 4≤t≤6, v(t) decreases linearly from 5 at t=4 to −3 at t=6.
• v(t)=−3 for t>6.
The position of the car at time t is s(t), and s(0)=10 meters.
(a) Identify the time intervals on which the car is moving forward and the intervals on which it is moving backward. Explain how you reached your conclusions.
(b) Compute s(6) and s(9). Show all steps, including any geometric area calculations used in your work.
(c) Determine whether the car ever changes direction. Justify your answer using the given velocity information.