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Unformatted text preview: Practice Midterm 1 Solutions April 18, 2009 Problem 1 : A sprinter accelerates from rest to top speed with an accel- eration of 3 . 8 m/s 2 . After achieving the top speed in 2 . 5 seconds, he runs the remainder of the race at this top speed. The total race is 100 meters on a straight track. a) What is his top speed? b) What amount of time does he take to complete the race? c) What is his average speed during the race? d) What is his average acceleration during the race? Solution : a) Top speed is given by: v f- v i t f- t i = a, v f = (3 . 8 m/s 2 )(2 . 5 s ) = 9 . 5 m/s b) The time to reach top speed is 2 . 5 seconds. In that time, the sprinter covers x = 1 2 a * t 2 = 11 . 88 meters. There are 100- 11 . 88 = 88 . 12 meters remaining in the race. That can be covered in time given by: t remaining = d remaining v = 88 . 12 9 . 5 = 9 . 28 s . The total time to complete the race is then 11 . 78 s . c) Average speed during the race is given by x f- x i t f- t f = 100- 11 . 78- = 8 . 49 m/s d) Average acceleration is (like average speed) given by: v f- v i t f- t i = 9 . 5- 11 . 78- = 0 . 81 m/s 2 ....
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