Question

7. Along the eastern shore of Lake Michigan from Lake Macatawa (near Holland) to Grand Haven, there is a bike path that runs almost directly north-south. For the purposes of this problem, assume the road is completely straight, and that the function s(t) tracks the position of the biker along this path in miles north of Pigeon Lake, which lies roughly halfway between the ends of the bike path. 4.1 Determining distance traveled from velocity Suppose that the biker’s velocity function is given by the graph in Figure 4.1.10 on the time interval 0 ? t ? 4 (where t is measured in hours), and that s(0) = 1. Figure 4.1.10: The graph of the biker’s velocity, y = v(t), at left. At right, axes to plot an approximate sketch of y = s(t). a. Approximately how far north of Pigeon Lake was the cyclist when she was the greatest distance away from Pigeon Lake? At what time did this occur? b. What is the cyclist’s total change in position on the time interval 0 ? t ? 2? At t = 2, was she north or south of Pigeon Lake? c. What is the total distance the biker traveled on 0 ? t ? 4? At the end of the ride, how close was she to the point at which she started? d. Sketch an approximate graph of y = s(t), the position function of the cyclist, on the interval 0 ? t ? 4. Label at least four important points on the graph of s.

          7. Along the eastern shore of Lake Michigan from Lake Macatawa (near Holland) to Grand Haven, there is a bike path that runs almost directly north-south. For the purposes of this problem, assume the road is completely straight, and that the function s(t) tracks the position of the biker along this path in miles north of Pigeon Lake, which lies roughly halfway between the ends of the bike path.

4.1 Determining distance traveled from velocity

Suppose that the biker’s velocity function is given by the graph in Figure 4.1.10 on the time interval 0 ? t ? 4 (where t is measured in hours), and that s(0) = 1.

Figure 4.1.10: The graph of the biker’s velocity, y = v(t), at left. At right, axes to plot an approximate sketch of y = s(t).

a. Approximately how far north of Pigeon Lake was the cyclist when she was the greatest distance away from Pigeon Lake? At what time did this occur?
b. What is the cyclist’s total change in position on the time interval 0 ? t ? 2? At t = 2, was she north or south of Pigeon Lake?
c. What is the total distance the biker traveled on 0 ? t ? 4? At the end of the ride, how close was she to the point at which she started?
d. Sketch an approximate graph of y = s(t), the position function of the cyclist, on the interval 0 ? t ? 4. Label at least four important points on the graph of s.

7. Along the eastern shore of Lake Michigan from Lake Macatawa (near Holland) to Grand Haven, there is a bike path that runs almost directly north-south. For the purposes of this problem, assume the road is completely straight, and that the function s(t) tracks the position of the biker along this path in miles north of Pigeon Lake, which lies roughly halfway between the ends of the bike path.

4.1 Determining distance traveled from velocity

Suppose that the biker’s velocity function is given by the graph in Figure 4.1.10 on the time interval 0 ? t ? 4 (where t is measured in hours), and that s(0) = 1.

Figure 4.1.10: The graph of the biker’s velocity, y = v(t), at left. At right, axes to plot an approximate sketch of y = s(t).

a. Approximately how far north of Pigeon Lake was the cyclist when she was the greatest distance away from Pigeon Lake? At what time did this occur?
b. What is the cyclist’s total change in position on the time interval 0 ? t ? 2? At t = 2, was she north or south of Pigeon Lake?
c. What is the total distance the biker traveled on 0 ? t ? 4? At the end of the ride, how close was she to the point at which she started?
d. Sketch an approximate graph of y = s(t), the position function of the cyclist, on the interval 0 ? t ? 4. Label at least four important points on the graph of s.

Added by Amber W.

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