Chapter 2:
Velocity
Assignment 1
Simple Motion Maps (a)
1
The Table gives the position and time of an arrow during a 4.0-second flight. (a) Draw a motion map of the arrow's flight. make sure the motion map is drawn to scale (b) What is the arrow’s position at t1 = 1.5 s? (b) What is the arrow's position at t2 = 3.0 s? (c) What is the arrow's displacement between t1 and t2? (d) What is the time interval corresponding to this displacement?
4
If the average velocity of a duck is zero in a given time interval, what can you say about the displacement of the duck for that interval? Answer the duck’s displacement must also be zero
5
Does knowing the displacement between the positions of two objects give you enough information to locate the objects? Explain. Answer No, because a single displacement value could correspond to a variety of different positions of the objects.
6
Answer (a) (b) (c) (d) (e) 2
Motion Map Drawing 85.30 m 154.20 m 68.9 m 1.5 sec
Two identical sailboats with different colored sails are traveling to the right in still water. The positions of the sailboats at successive one-second time intervals are shown in the diagram . Use a scale of 1 mm = 10 meters. (a) Make a table of the sailboat positions at each interval of time. (b) Which sailboat has the greater displacement after 1 second (c) Which sailboat has the greater displacement after 2 seconds (d) Which sailboat has the greater displacement after 3 seconds?
A girl winds up a toy car and places it on the floor. When she lets go of the car it moves as shown in the strobe picture. Her brother releases a similar car in the opposite direction The cars are shown at 2 s intervals Make a table comparing the position and times of the two cars shown in the motion map. Note: The intervals shown on the picture represent 1.5 meters. Answer
7 Answer
3
The hair is traveling at 1 m/s while the turtle is traveling at .5 m/s. Draw a motion map to show when the hair catches the turtle.
Answer
While John is traveling along a straight interstate highway, he notices that the mile marker reads 260. John travels until he reaches the 150-mile marker and then retraces his path to the 175-mile marker. (a) What is John's displacement from the 260-mile marker? (b) What is Jon's distance from the 260-mile mark? (c) What is the total distance that John traveled? Answer (a) -85 mi. (b) +85 mi. (c) 135 mi.
8
Here are three pairs of initial and final positions, respectively, along an x axis. Which pairs give a negative displacement: (a) -3 m, +5 m; (b) -3 m, -7 m; (c) 7 m, -3 m?
Answer b and c
Chapter 2:
Velocity
Assignment 3
Average Speed & Average Velocity (c)
9
10
11
Eugene is 75.0 km due south of Salem. If Joe rides from Salem to Eugene on his bike in 6.00 h, what is his average velocity?
15
Answer
Answer
12.5 km/h 3.47 m/s to the south
4.3 km/hr 7.2 x 10-2 km/min 1.2 m/s to the north
The Olympic record for the marathon is 2 h, 9 min, 21 s. The marathon distance is 42.19 km. Determine the average speed in m/s of a runner achieving this record.
16
Answer
5.436 m/s
75.73 km/h 5.3 m/s to the east
In a 4-hour period, a hiker walked 5.0-km north during the first hour and 4.4-km south during the second hour. After resting for an hour, the hiker walked 4.6 south km during the fourth hour. (a) What was the average velocity during the first two hours; (b) What was the average velocity during the first three hours; (c) What was the average velocity during the entire fourhour period?
(a) 0.3 km/hr (b) 0.2 km/hr N (c) -1 km/hr
17
The Sears Tower in Chicago is 443 m tall. Joe wants to set the world's stair-climbing record and runs all the way up to the roof of the tower in 12.0 min. On the way back down, he is so tired that it takes him twice as long to descend. What is Joe's average speed (in m1s) during the entire trip?
10 km/hr 5.3 m/s to the east 18
6.02 m/s to the west 19
Heather and Matthew take 34 min to walk eastward along a straight road to a store 2.0 km away. What is their average velocity in m/s?
(a) 2.50 m/s to the south (b) 2.27 m/s to the north (c) 0.0 m/s (d)
0.98 m/s to the east
Answer 7.2 x 10-2 km/min 1.2 m/s North.
An athlete swims from the north end to the south end of a 50.0-m pool in 20.0 s and makes the return trip to the starting position in 22.0 s. (a) What is the average velocity for the first half of the swim? (b) What is the average velocity for the second half of the swim? (c) What is the average velocity for the roundtrip? (d) What is the average speed for the entire swim? Answer
Answer
If a bus stop is 0.68 km down he street from the museum and it takes you 9.5 minutes to walk north frm the bus stop to the museum entrance, what is your average velocity?
During a race on level ground, Andrea covers 825 m in 137 s while running due west. Find Andrea’s average velocity. Answer
0.410 m/s
14
If you live 10.0 km from your school and the bus takes 0.53 h to reach the school driving due east, what is the average velocity of the bus? Answer
Answer
13
El Paso is 1142 km south of Denver. If a bus makes the trip in 15.08 h, what is its average velocity?
Answer
Answer
12
If the bus stop is 0.68 km down the street from the museum and it takes you 9.5 min to walk north from the bus stop to the museum entrance, what is your average velocity?
20
A cross-country runner runs 5.0 km east along the course, then turns around and runs 5.0 km west along the same path. She returns to the starting point in 40 min. (a) What is her average speed? (b) What is her average velocity? Answer (a) 15 km/h 4.17 m/s (b) 0
Chapter 2:
Velocity
Assignment 3 Unit 1 Velocity
21
The figure shows four paths along which objects move from a starting point to a final point, all in the same time interval. The paths pass over a grid of equally spaced straight lines. (a) Rank the paths according to the average velocity of the objects, greatest first. (b) Rank the paths according to the average speed of the objects, greatest first.
24
You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. (a) What is your average speed from San Antonio to Houston? (b) What is your average speed from Houston back to San Antonio? (c) What is your average speed for the entire trip? (d) What is your average velocity for the entire trip? (e) Sketch x versus t for (a), assuming the motion is all in the positive x direction. Indicate how the average velocity can be found on the sketch. Answer (a) 73km/h; (b) 68km/h; (c) 70km/h; (d) 0
Answer (a) all tie; (b) 4, tie of 1 and 2, then 3 22
23
You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. (a) What is your average speed from San Antonio to Houston? (b) What is your average speed from Houston back to San Antonio? (c) What is your average speed for the entire trip? (d) What is your average velocity for the entire trip? (e) Sketch x versus t for (a), assuming the motion is all in the positive x direction. Indicate how the average velocity can be found on the sketch.
25
You are to drive to an interview in another town, at a distance of 300 km on an expressway. The interview is at 11:15 A.M. You plan to drive at 100 km/h, so you leave at 8:00 A.M. to allow some extra time. You drive at that speed for the first 100 km, but then construction work forces you to slow to 40 km/h for 40 km. What would be the least speed needed for the rest of the trip to arrive in time for the interview? Answer 128 km/h
26
Simpson drives his car with an average velocity of 24 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway?
Answer
Answer
(a) 73km/h; (b) 68km/h; (c) 70km/h; (d) 0
6.5 h 27
You are to drive to an interview in another town, at a distance of 300 km on an expressway. The interview is at 11:15 A.M. You plan to drive at 100 km/h, so you leave at 8:00 A.M. to allow some extra time. You drive at that speed for the first 100 km, but then construction work forces you to slow to 40 km/h for 40 km. What would be the least speed needed for the rest of the trip to arrive in time for the interview? Answer 128 km/h
The peregrine falcon is the fastest of flying birds (and, as a matter of fact, is the fastest living creature). A falcon can descend with a speed of 2.50 x 102 km/h. If a falcon flies at this speed for 2.00 s and then flies another 1.00 x 102 m in 2.50 s, what is the falcon's average speed for the entire flight? Answer 191 km/h 53.1 m/s
28
A bus traveled south along a straight path for 3.2 h with an average velocity of 88 km/h, stopped for 20.0 min, then traveled south for 2.8 h with an average velocity of 75 km/h. (a) What is the average velocity for the total trip? (b) What is the displacement for the total trip? Answer (a) 78 km/h to the south (b) 490 km to the south
Chapter 2:
Velocity
Assignment 4
Manipulating Velocity, Time and Displacement (d)
29
The black mamba is one of the world's most poisonous snakes, and with a maximum speed of 18.0 km/h, it is also the fastest. Suppose a mamba waiting in a hideout sees prey and begins slithering toward it at its maximum speed. After 2.50 s, the mamba realizes that its prey can move faster than it can. The snake then turns around and slowly returns to its hide-out in 12.0 s. (a) What is the mamba's average speed? (b) What is the mamba's average velocity?
33
Answer
The figure is a graph of a particle's position along an x axis versus time. (a) At time t = 0, what is the sign of the particle's position? (b) Is the particle's velocity positive, negative, or 0 at t = 1 s? (c) Is the particle's velocity positive, negative, or 0 at t = 2 s? (d) Is the particle's velocity positive, negative, or 0 at t = 3 s? (e) How many times does the particle go through the point x = 0?
(a) 1.72 m/s (b) 0 m/s 30
Sally travels by car from one city to another. She drives for 30.0 min at 80.0 km/h, 12.0 min at 105 km/h, and 45.0 min at 40.0 km/h, and she spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip. (b) Determine the average velocity for the trip. (c) Determine the total distance traveled Answer Answer
(a) 535 km/h (b) (c) 91.0 km 31
(a) negative; (b) positive; (c) zero; (d) negative; (e) twice
What is the shortest possible time in which a bacterium could move at a speed of 3.5 mm/s across a petri dish with a diameter of 8.4 cm? Answer
34
24 s 32
In 1 km races, runner 1 on track 1 (with time 2 min, 27.95 s) appears to be faster than runner 2 on track 2 (2 min, 28.15 s). However, length L2 of track 2 might be slightly greater than length L1 of track 1. How large can L2 - L1 be for us still to conclude that runner 1 is faster?
A child can push a shopping cart at a speed of 1.5 m/s. How long would it take this child to push the cart down an aisle with a length of 9.3 m?
Answer
Answer
1.4 m
6.2 s 35
Two boys start running straight toward each other from two points that are 100 m apart. One runs with a speed of 5 m/s, while the other moves at 7 m/s. How close are they to the slower one's starting point when they reach each other?
Answer
Chapter 2:
Velocity
Assignment 5
Position-Time Graphs (e)
36
37
The position of an object during a 20-second time interval is shown in the figure (a) What is the object’s path length between t = 0 s and t = 5 s. (b) What is the object’s path length between t = 5 s and t = 10 s. (c) What is the object’s path length between t = 10 s and t = 15 s. (d) What is the object’s path length between t = 15 s and t = 20 s. (e) What is the object’s path length between t = 0 s and t = 20 s
38
The position of an object during a 20-second time interval is shown in the figure. (a) What is the object’s displacement between t = 0 s and t = 5 s. (b) What is the object’s displacement between t = 5 s and t = 10 s. (c) What is the object’s displacement between t = 10 s and t = 15 s. (d) What is the object’s displacement between t = 15 s and t = 20 s. (e) What is the object’s displacement between t = 0 s and t = 20 s
Answer
Answer
(a) (b) (c) (d) (e)
(a) (b) (c) (d) (e)
10 m 30 m 0m 40 m 80 m distance
Use the figure to answer the following questions? (a) What is the total distance traveled during the recorded time interval? (b) What is the displacement?
39
10 m 30 m 0m -40 m 0 displacement
The figure is a graph of the position of an object over a given time interval. (a) Use the position-time graph to find how far the object travels between t = 0 s and t = 40 s (b) Use the position-time graph to find how far the object travels between t = 40 s and t = 70 s (c) Use the position-time graph to find how far the object travels between t = 90 s and t = 100 s
Answer 5.0 m +5.0 m
Answer (a) 400 m (b) 0 (c) - 200 m
Chapter 2:
Velocity
Assignment 6
Slope of Position-Time Graphs (f)
40
A position-time graph of an object is shown in the figure . (a) Use the position-time graph to find the object's velocity between t = 0 s and t = 5 s. (b) Use the position-time graph to find the object's velocity between t = 5 s and t = 10 s. (c) Use the position-time graph to find the object's velocity between t = 10 s and t = 15 s. (d) Use the position-time graph to find the object's velocity between t = 15 s and t = 20 s. (e) Use the position-time graph to find the object's velocity between t =0 s and t = 20 s
42
The figure is the position-time graph for a squirrel running along a clothesline. (a) What is the squirrel's displacement during the time interval from t = 0.0 s to t = 3.0 s? (b) What is the squirrel's average velocity during this interval?
Answer (a) -2.0 m (b) -.67 m/s 43 Answer (a) (b) (c) (d) (e) 41
2 m/s 6 m/s 0 m/s -8 m/s 0 m/s
The position of an object over time is shown in the figure . (a) Find the average velocity of an object between t = 10 and 12 s (b) Find the average velocity of an object between t = 14 and 18 s (c) Find the average velocity of an object between t = 20 and 24 s (d) Find the average velocity of an object between t = 26 and 30 s
A position-time graph of an object is shown in the figure . (a) Use the position-time graph to find the object's velocity between t = 0 s and t = 5 s. (b) Use the position-time graph to find the object's velocity between t = 5 s and t = 10 s. (c) Use the position-time graph to find the object's velocity between t = 10 s and t = 15 s. (d) Use the position-time graph to find the object's velocity between t = 15 s and t = 20 s. (e) Use the position-time graph to find the object's velocity between t =0 s and t = 20 s
Answer
Answer (a) (b) (c) (d)
+ 2.5 m/s -1.25 m/s -3.25 m/s +.4 ms/
(a) (b) (c) (d) (e)
2 m/s 6 m/s 0 m/s -8 m/s 0 m/s
Chapter 2:
Velocity
Assignment 7
Instantaneous Velocity (g)
44
From the position-time graph shown in the figure construct a table showing the average velocity of the object during each 10-s interval over the entire 100 s.
46
A position time graph for an object is shown in the figure . (a) Obtain the velocity of the object at 1 s (b) Obtain the velocity of the object at 2 s (c) Obtain the velocity of the object at 4 s
Answer Answer 0-10 10 m/s 10-20 10 m/s 20-30 10 m/s 30-40 10 m/s 40-50 0 m/s 50-60 0 m/s 60-70 0 m/s 70-80 -10 m/s 80-90 -10 m/s 90-100 -20 m/s 45
(a) -.666 m/s (b) -4m/s (c) -1.25 m/s 47
An object moves as shown in the graph shown in the figure . Calculate the object's velocity at t = 3 s.
A position time graph for an object is shown in the figure . (a) Determine the slope of the object at 1 s (b) Determine the slope of the object at 4 s.
Answer -10 m/s 48
On the position-time graph shown in the figure , what represents the velocity?
Answer (a) 6.4 m/s (b) 2.4 m/s
Answer The slope of the line at each point.
Chapter 2:
Velocity
Assignment 7
Instantaneous Velocity (g)
49
The position-time graph for a bug crawling along a line is shown in the figure . Determine whether the velocity is positive, negative, or zero at each of the times marked on the graph.
51
The figures shows position-time graphs of the straight-line movement of two brown bears in wildlife preserve. (a) Which bear has the greater average velocity over the entire period? (b) Which bear has the greater velocity at t= 10.0 min? (c) Is the velocity of bear A always positive? Explain (d) Is the velocity of bear B ever negative? Explain.
Answer t1; negative t2; positive t3; positive t4; negative t5; zero 50
Answer
Use the position-time graph in the figure to answer the following questions: (a) During which time interval(s) is the magnitude of the velocity (speed) decreasing? (b) During which time interval(s) is the magnitude of the velocity (speed) increasing
(a) (b) (c) (d) 52
Bear B Bear A No No
A position time graph for an object is shown in the figure. (a) Determine the slope of the object at 2 s (b) Determine the slope of the object at 3 s.
Answer (a) 0 to t1 t1 to t2 t3 to t4 t4 to t5 (b) t1 to t2 t2 to t3 t3 to t4
Answer (a) (b)
Chapter 2:
Velocity
Assignment 7
Instantaneous Velocity (g)
53
A position time graph for an object is shown in the figure . (a) What is the average velocity between 3 s and 5 s? (b) What is the average velocity between 0 s and 4 s?
55
For the position time graph shown in the figure, determine the velocity at t = 2 sec.
Answer Answer (a) 7.5 m/s (b) 7.5 m/s 56 54
A position time graph for an object is shown in the figure . (a) Obtain the average velocity of the object between 1s and 4s (b) Obtain the average velocity of the object between 0.2 s and 3s (c) Obtain the average velocity of the object between 1.5 s and 3.4 s
Simpson drives his car with an average velocity of 24 m/s toward the east. He drives 560 km on a perfectly straight highway (a) How much time would Simpson save by increasing his average velocity to 26 m/s east? (b) Sketch a position time graph of his two speeds. Answer 0.5 h
57
To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 1600 m. (a) If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event to qualify? (b) Show how you would solve this problem using a graph. Answer 280 km/r
Answer
58
(a) (b) (c)
Emily takes a trip, driving with a constant velocity of 89.5 km/h to the north except for a 22.0-min rest stop. If Emily's average velocity is 77.8 km/h to the north, how long does the trip take? Answer 2.81 h
59
A tortoise can run with a speed of 10.0 cm/s, and a hare can run exactly 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.00 min. The tortoise wins by 20.0 cm. (a) Draw a position time graph for both the tortoise and the hair. Put both critters on the same axis. (b) How long does the race take? (c) What is the length of the race? (d) Solve the problem using algebra. Answer (a) 126 s (b) 1260 cm
Chapter 2:
Velocity
Assignment 8
Modeling Motion With Words, Graphs, Equations and Motion Maps. (h)
60
Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 9.0 km/h due east. Runner B is initially 5.0 km east of the flagpole and is running with a constant velocity of 8.0 km/h due west. (a) Draw a position time graph for the runners (b) How far are the runners from the flagpole when their paths cross? (c) Solve the problem by algebra. Answer 0.2 km west of the flagpole
61
Two students walk in the same direction along a straight path, at a constant speed Answer (a) 460 s (b) 570 m
62
To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 1600 m. (a) If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event to qualify? (b) Show how you would solve this problem using a graph. Answer 280 km/r
63
Emily takes a trip, driving with a constant velocity of 89.5 km/h to the north except for a 22.0-min rest stop. If Emily's average velocity is 77.8 km/h to the north, how long does the trip take? Answer 2.81 h
