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Unformatted text preview: sousse (res2468) – HW 2 – Kleinman – (58225) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. This HW assignment covers Ch. 2. 001 10.0 points Two ants race across a table 74 cm long. One travels at 5 . 25 cm / s and the other at 3 cm / s. When the first one crosses the finish line, how far behind is the second one? Correct answer: 31 . 7143 cm. Explanation: Let : ℓ = 74 cm , v 1 = 5 . 25 cm / s , and v 2 = 3 cm / s . You first have to compute the time it takes the first (faster) ant to cross the finish line: t = ℓ v 1 . Then you must compute the distance the slower ant covers in that time s 2 = v 2 t = v 2 ℓ v 1 . The slower ant is ℓ- s 2 = ℓ- v 2 ℓ v 1 = (74 cm)- (3 cm / s) (74 cm) (5 . 25 cm / s) = 31 . 7143 cm from the finish line when the faster one crosses it. 002 10.0 points On a drive from your ranch to Austin, you wish to average 56 mph. The distance from your ranch to Austin is 96 miles. However, at 48 miles (half way), you find you have averaged only 42 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 56 mph? Correct answer: 84 mph. Explanation: Let t denote the total time, d the total distance, and v the average velocity over the total distance. Let t 1 denote the time over the first half, d 1 the first half distance, and v 1 the average velocity of the first half. Let t 2 denote the time over the second half, d 2 the second half distance, and v 2 the average velocity of the second half. The change in velocity occurs at d 1 , therefore d 2 = d- d 1 . (1) Average speed is v ≡ Δ d Δ t = d t . Thus t 1 = d 1 v 1 (2) t = d v . (3) The total time t = t 1 + t 2 , so t 2 = t- t 1 = d v- d 1 v 1 (4) since d 2 = v 2 t 2 v 2 = d 2 t 2 ≈ 84 mph . Notice that the formula for average velocity when acceleration is constant: v = v 1 + v 2 2 yields: v 2 = 2 v- v 1 = 2(56 mph)- 42 mph = 70 mph an incorrect answer!!!! Do you know why this formula is incorrect? What is the acceleration at the halfway point? What is the acceler- ation over the rest of the distance? Is the acceleration constant? For constant acceler- ation v = v + at . The graph of velocity vs time is a straight line. For this problem the graph of velocity vs time is a step function. 003 10.0 points sousse (res2468) – HW 2 – Kleinman – (58225) 2 A car travels along a straight stretch of road. It proceeds for 17 . 2 mi at 50 mi / h, then 21 . 8 mi at 49 mi / h, and finally 42 . 6 mi at 33 . 6 mi / h. What is the car’s average velocity during the entire trip? Correct answer: 39 . 6741 mi / h. Explanation: The total distance the car traveled is Δ d = d A + d B + d C = 81 . 6 mi The total time the car spent on the road is Δ t = d A v A + d B v B + d C v C = 17 . 2 mi 50 mi / h + 21 . 8 mi 49 mi / h + 42 . 6 mi 33 . 6 mi / h = 2 . 05676 h ....
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This note was uploaded on 04/08/2009 for the course 303K 303K taught by Professor Kleinman during the Spring '09 term at University of Texas.
- Spring '09