College Physics, Young,Geller CH02-CH05

College Physics, Young,Geller CH02-CH05 - MOTION ALONG A...

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Unformatted text preview: MOTION ALONG A STRAIGHT LINE 2 8. A 9. B 10. C 11. A 12. A, C, D 13. B, D Answers to Multiple-Choice Problems 1. C, D 2. C 14. D 15. C 3. C, D 4. A, B 5. D 6. C 7. A, D Solutions to Problems 2.1. Set Up: Let the 1x direction be to the right in the figure. Solve: (a) The lengths of the segments determine the distance of each point from O: xA 5 25 cm, xB 5 145 cm, xC 5 115 cm, and xD 5 25 cm. (b) The displacement is D x; the sign of D x indicates its direction. The distance is always positive. (i) A to B: D x 5 xB 2 xA 5 145 cm 2 1 25 cm 2 5 150 cm. Distance is 50 cm. (ii) B to C: D x 5 xC 2 xB 5 115 cm 2 45 cm 5 230 cm. Distance is 30 cm. (iii) C to D: D x 5 xD 2 xC 5 25 cm 2 15 cm 5 220 cm. Distance is 20 cm. (iv) A to D: D x 5 xD 2 xA 5 0. Distance 5 2 1 AB 2 5 100 cm. Reflect: When the motion is always in the same direction during the interval the magnitude of the displacement and the distance traveled are the same. In (iv) the ant travels to the right and then to the left and the magnitude of the displacement is less than the distance traveled. 2.2. Set Up: From the graph the position xt at each time t is: x1 5 1.0 m, x2 5 0, x3 5 21.0 m, x4 5 0, x8 5 6.0 m, and x10 5 6.0 m. Solve: (a) The displacement is D x. (i) D x 5 x10 2 x1 5 15.0 m; (ii) D x 5 x10 2 x3 5 17.0 m; (iii) D x 5 x3 2 x2 5 21.0 m; (iv) D x 5 x4 2 x2 5 0. (b) (i) 3.0 m 1 1.0 m 5 4.0 m; (ii) 1.0 m 1 1.0 m 5 2.0 m; (iii) zero (stays at x 5 6.0 m) 2.3. Set Up: Let the 1x direction be to the right. xA 5 2.0 m, xB 5 7.0 m, xC 5 6.0 m. Solve: Average velocity is xC 2 xA 16.0 m 2 2.0 m Dx 5 5 5 1.3 m / s. Dt Dt 3.0 s distance 4.0 m 1 1.0 m 1 1.0 m Average speed 5 5 5 2.0 m / s time 3.0 s vav-x 5 Reflect: The average speed is greater than the magnitude of the average velocity. 2.4. Set Up: The distance traveled is 2650 miles and the displacement is 1000 miles. Solve: (a) time 5 12 weeks 1 168 h / week 2 5 2016 h Average speed 5 2650 miles distance 5 5 1.3 mi / h time 2016 h 2-1 ...
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