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Unformatted text preview: Practice Problems for Derek’s Midterm 1 Review Session Problem 1) The graph represents the position of a bicyclist who, starting from rest at t = 0, travels along a straight path. Between t = 0 and t = 9 s, the mathematical equation describing her position is x = t 2 , with x in feet and t in seconds. (a) Make a rough sketch of the bicycle’s velocity vs. time. (b) What is the cyclist’s exact velocity at time t = 3 seconds? At time t = 6 s? (c) What total distance did the cyclist travel between t = 0 and t = 15 s? (d) Let me now add some additional information about the cyclist’s trip. While riding along the path, she suddenly noticed a skunk ahead of her. But a few seconds later, the skunk wandered back into the woods. From looking at the x vs. t graph, guess when the cyclist first saw the skunk, and when the skunk was safely out of the way. Problem 2) An astronaut on Mars throws a ball straight up. The ball leaves his hand at time t = 0, with initial speed 20 m/s. Due to gravity, the ball gradually slows down. In fact, for reasons we will soon study in detail, this ball’s velocity, as a function of time, is approximately given by v = 20 - 4t , with t in seconds and v in meters per second. (a) At what time does the ball reach its maximum height off the ground? (b) What is the ball’s maximum height? In other words, how far up does the ball travel from the astronaut’s hand?...
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This note was uploaded on 04/29/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at University of California, Berkeley.
- Spring '06