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Unformatted text preview: (9/30/08) Math 10B. Lecture Examples. Section 5.1. How do we measure distance traveled? † Example 1 At 10:00 AM one morning a truck driver is 100 miles east of his home town. He drives 75 miles per hour toward the east for two hours to make a delivery. Next, he drives west at 50 miles per hour for two hours to make another delivery and then drives east at 50 miles per hour for two more hours. According to this mathematical model, his velocity toward the east is the step function of Figure 1 with t = at 10 AM. (a) How far is he from his home town at t = 6 ? (b) How is the answer to part (a) related to the areas of the rectangles in Figure 2? t 1 2 3 4 5 6 v (miles per hour)- 50 25 75 (hours) v = v ( t ) t 1 5 6 v (miles per hour)- 50 25 75 (hours) A B C FIGURE 1 FIGURE 2 Answer: (a) At t = 6, the driver is 250 mileseast of his home town. (b) His location at t = 6 equals his location at t = 0 plus the the sum of the areas of rectangles A and C in Figure 2, minus the area of rectangle B...
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