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Chapter 2 continued 42, If you know the positions of a moving object at two points along its path, and you also know the time it took for the object to get from one point to the other, can you determine the particle’s instantaneous velocity? Its average velocity? Explain. (2.4) It is possible to calculate the average velocity from the information given, but it is not possible to find the instanta- neous velocity. Applying Concepts page 52 43. 44, 45, Test the following combinations and explain why each does not have the proper- ties needed to describe the concept of veloc- ity: Ad + At, Ad — At, Ad X At, At/Ad. Ad + Atincreases when either term increases. The sign of Ad — At depends upon the relative sizes of Ad and At. Ad X Atincreases when either increas- es. At/Ad decreases with increasing displacement and increases with increasing time interval, which is back- wards from velocity. Football When can a football be consid- ered a point particle? A football can be treated as a point particle if its rotations are not important and if it is small in comparison to the distance it moves — for distances of 1 yard or more. When can a football player be treated as a point particle? A football player can be treated as a point particle if his or her internal motions are not important and if he or she is small in comparison to the dis- tance he or she moves — for distances of several yards or more. 46. &7. Figure 2-26 is a graph of two people running. =] }”/d7 et M S Position (m) Time (s) | Figure 2-26 a. Describe the position of runner A relative to runner B at the y-intercept. Runner A has a head start by four units. b. Which runner is faster? Runner B is faster, as shown by the steeper slope. ¢. What occurs at point P and beyond? Runner B passes runner A at point P. The position-time graph in Figure 2-27 shows the motion of four cows walking from the pasture back to the barn. Rank the cows according to their average velocity, from slowest to fastest. Position (m) | Time (s) ® Figure 227 Moolinda, Dolly, Bessie, Elsie
Chapter 2 continued 48. Figure 2-28 is a position-time graph for a rabbit running away from a dog. 3 T £, : ] £ - & o 1 2 3 Time (s) = Figure 228 a. Describe how this graph would be different if the rabbit ran twice as fast. The only difference is that the slope of the graph would be twice as steep. b. Describe how this graph would be dif- ferent if the rabbit ran in the opposite direction. The magnitude of the slope would be the same, but it would be negative. Mastering Problems 2.4 How Fast? page 53 Level 1 49. A bike travels at a constant speed of 4.0 m/s for 5.0 s. How far does it go? d=vt = (4.0 m/s)(5 5) =20x10" m 50. Astronomy Light from the Sun reaches Farth in 8.3 min. The speed of light is 3.00% 108 m/s. How far is Earth from the Sun? d=ut = (3.00x10° m/s)(8.3 min) o) =15x10" m Level 2 A car is moving down a street at 55 km/h. A child suddenly runs into the street. If it takes the driver 0.75 s to react and apply the brakes, how many meters will the car have moved before it begins to slow down? d=vt = (55 km/h)(0.75 a)( =11m 1000 my_th ) 1 km /\3600 s Nora jogs several times a week and always keeps track of how much time she runs each time she goes out. One day she forgets to take her stopwatch with her and wonders if there’s a way she can still have some idea of her time. As she passes a particular bank, she remembers that it is 4.3 km from her house. She knows from her previous training that she has a consistent pace of 4.0 m/s. How long has Nora been jogging when she reaches the bank? d=vt @3k ) 4.0 m/s =1075s = (1075 5)( ‘o) =18 min Level 3 53. Driving You and a friend each drive 50.0 km. You travel at 90.0 km/h; your friend travels at 95.0 km/h. How long will your friend have to wait for you at the end of the trip? d=vt f = d_ 500km 17 v 90.0 km/h =0556h _d_ 500km L v 95.0 kmh =0526h —t= - 60 min) t, — t, = (0556 h — 0.526 h) %" =1.8 min
Chapter 2 continued Mixed Review pages 53-54 Level 1 54. Cycling A cyclist maintains a constant velocity of +5.0 m/s. At time t = 0.0's, the cyclist is +250 m from point A. a. Plot a position-time graph of the cyclist's location from point A at 10.0-s intervals for 60.0s. 550 F-=r--rere Position (m) oINS 250 200 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Time (s) b. What is the cyclist’s position from point Aat 60.0 s? 550 m ¢. What is the displacement from the starting position at 60.0 s? 550 m — 250 m = 3.0x102 m 55. Figure 2-29 is a particle model for a chicken casually walking across the road. Time inter- vals are every 0.1 5. Draw the corresponding position-time graph and write the equation 1o describe the chicken’s motion. This side The other side ecccc00000c0000000000 Time intervals are 0.1s. w Figure 229 d The other side This side t 0 195 The equation is Ad = vAL. 56. Figure 2-30 shows position-time graphs for Joszi and Heike paddling canoes in a local river. 18 = 16 T 14 ;E: 12 < 10 8 — 4 - — 2 0 05 10 15 20 25 Time (h) m Figure 2-30 a. At what time(s) are Joszi and Heike in the same place? ~ 10h b. How much time does Joszi spend on the river before he passes Heike? 45 min c. Where on the river does it appear that there might be a swift current? from 6.0 to 9.0 km from the origin Level 2 57. Driving Both car A and car B leave school when a stopwatch reads zero. Car A travels at a constant 75 km/h, and car B travels at a constant 85 km/h. a. Draw a position-time graph showing the motion of both cars. How far are the two cars from school when the stop- watch reads 2.0 h? Calculate the dis- tances and show them on your graph. dp = vpt = (75 km/h)(2.0 h) =150 km dg = vgt = (85 km/h)(2.0 h) =170 km
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Chapter 2 continued 255¢ 200 170f=====pmm = 150 Position (km) S H H | H | i 16 30 Time (h) b. Both cars passed a gas station 120 km from the school. When did each car pass the gas station? Calculate the times and show them on your graph. _d _120km _ =5, = 75kmn = 16h tg=d = 120km g4y vg 85 km/h 58. Draw a position-time graph for two cars traveling to the beach, which is 50 km from school. At noon, Car A leaves a store that is 10 km closer to the beach than the school is and moves at 40 km/h. Car B starts from school at 12:30 p.M. and moves at 100 km/h. ‘When does each car get to the beach? GO Position (m) 1017 {‘/— - 0 Noon 12/ 122 12% 129 12% 1%m Time Both cars arrive at the beach at 1:00 p.m. Level 3 59. Two cars travel along a straight road. When a stopwatch reads t = 0.00 h, car A is at dy = 48.0 km moving at a constant 36.0 km/h. Later, when the watch reads £=0.50 h, car B is at d = 0.00 km moving Position (km) at 48.0 kn/h. Answer the following ques- tions, first, graphically by creating a posi- tion-time graph, and second, algebraically by writing equations for the positions dy and dy; as a function of the stopwatch time, £. a. What will the watch read when car B passes car A? 300.0 250.0 200.0 150.0 100.0 50.0, L | ~1.000.00" 1.00 2,00 3.00 4.00 500 6.00 7.00 Time (h) Cars pass when the distances are equal, dy = dy dp = 48.0 km + (36.0 km/h)t and dg = 0 + (48.0 km/h)(t — 0.50 h) 50 48.0 km + (36.0 km/h)t = (48.0 km/h)(t — 0.50 h) (48.0 km) + (36.0 km/h)t = (48.0 km/h)t — 24 km 72 km = (12.0 km/h)t t=6.0h b. At what position will car B pass car A? dp = 48.0 km + (36.0 km/h)(6.0 h) =2.6X10% km c. When the cars pass, how long will it have been since car A was at the reference point? d=vt sot=d - =9BOkm _ _ o0 km/h Car A has started 1.33 h before the clock started. t=60h+133h=73h
Chapter 2 continued ' 60. Figure 2-31 shows the position-time graph Position (m) depicting Jim’s movement up and down the aisle at a store. The origin is at one end of the aisle. 14.0 - ) | 12.0 -\ 10.0 Thinking Critically page 54 61. Apply Calculators Members of a physics class stood 25 m apart and used stopwatch- es to measure the time which a car traveling on the highway passed each person. Their data are shown in Table 2-3. 80 3 Table 2-3 } Position v. Time 60 Time (s) Position (m) 40 i 00 00 2.0 j —1 \~ 13 250 27 50.0 0.00 10.0 20.0 30.0 40.0 50.0 60.0 36 75.0 Time (s) 5.1 100.0 | Figure 2-31 . P 59 125.0 a. Write a story describing Jim's movements at the store that would correspond to the 70 1500 motion represented by the graph. 86 175.0 Answers will vary. 103 200.0 b. When does Jim have a position of 6.0 m? from 8.0 to 24.0 s, 53.0 to 56.0 s, and at43.0s ¢. How much time passes between when Jim enters the aisle and when he gets to a position of 12.0 m? What is Jim’s aver- age velocity between 37.0 s and 46.0 s? t=330s-240s=90s Using the points (37.0 s, 12.0 m) and (46.0's, 3.00 m) 9 _ 300m-120m 46.0s —37.0s Use a graphing calculator to fit a line to a position-time graph of the data and to plot this line. Be sure to set the display range of the graph so that all the data fit on it. Find the slope of the line. What was the speed of the car? 200.0 150.0 7 100.0 50.0 = e Position (m) 0.0 20 40 60 80 10.012.0 Time (s) The slope of the line and the speed of the car are 19.7 m/s. Apply Concepts You plan a car trip for which you want to average 90 km/h. You cover the first half of the distance at an average speed of only 48 km/h. What must your average speed be in the second half of the trip to meet your goal? Is this reason- able? Note that the velocities are based on half the distance, not half the time.