The picture shows the motion map of a car moving north.

Transcription

1 1 The Table gives the position and time of an arrow during a 4.0 second flight. Draw a motion map of the arrow's flight. make sure the motion map is drawn to scale What is the arrow s position at t 1 = 1.5 s? (c) What is the arrow's position at t 2 = 3.0 s? (d) What is the arrow's displacement between t 1 and t 2? (e) What is the time interval corresponding to this displacement? 3 The picture shows the motion map of a car moving north. Make a table of the car s time and position. What is the position of the car at 2 seconds? (c) What is the position of the car at 5 seconds? (d) What is the change in position between 0 and 3 seconds? (e) What is the change in position between 3 and 6 seconds? (f) What is the change in position between 6 and 9 seconds (g) What is another name for change in position? 2 Motion Map Drawing m (c) m (d) 70.9 m (e) 1.5 sec The picture shows a ball rolling along a table at 1 second time intervals. The position is measured using a 2 meter stick. Make a time position table of the ball shown in the picture. What is the scale of the drawing? 4 4 m/s north (c) 25 m north (d) 9 m north (e) 27 m north (f) 45 m north (g) displacement notes Time Position The diagram shows a motion map of a car moving east. Make a table of the car s time and position What is the car s position at 3 seconds? (c) What is the car s position at 5 seconds? (d) What is the car s displacement between 3 and 5 seconds? Allow +/- 3 time Position part B scale may vary a bit but its about 29 to 1 Sec Position ft (c) 125 ft (d) 80 ft

2 5 A stroboscopic photograph of a Dry Ice puck as it moves from left to right. The light flashed every tenth of a second and the scale is in centimeters. Make a time position table of the movement of the ice puck What is the scale of the diagram? 7 The table gives the position and time of an object during a 7.0 second time interval. Draw a motion map of the object s movement. Make sure the motion map is draw to scale. What is the object s position at t 1 = 2 s? (c) What is the object s position at t 2 = 5.0 s? (d) What is the object s displacement between t 1 and t 2? (e) What is the time interval corresponding to this displacement? Table Time position cm =.16 cm 6 The picture shows the movement of a ball. The light flashes every 1/10-second. Make a time position table of the movement of the ball. If the scale at the top represents a meter stick, what is the scale of the picture 7 m 0 m (c) -7 m (d) 3 sec Time Position to 1 8 Use the motion map showing three runners. Make a position time table for each runner (assume the time flashes are equal and the same for each runner) Make a position time graph for each runner. Place all three runners on the same graph. (c) Do Runners A, B and C ever meets at the same point? explain your answers. (c)

3 9 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. The car is shown at 2 s intervals Make a time position table of the toy car shown in the picture. Note: Each interval on the graph represents 0.5 meters Make a position time graph of the motion of the car? 11 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. Make a position-time graph of the two cars. (c) How can you compare the motion of the two cars on the same graph to see if the car is going at the same speed? (d) Draw the graph. 10 Time Position The picture shows Joey and Merinda racing around a lamp post and back to the sidewalk. While Joey is still running towards the street lamp, Merinda will pass him on her way back to the sidewalk. Make a position time table of Joey and Merinda Make a position time graph of Joey and Merinda (c) Make a motion map of Joey and Merinda racing by drawing symbols to show the positions of Merinda and Joey every second. We have drawn the first few symbols for you. (d) How far from the street lamp will this happen? (e) At what time will this happen? (f) What is their position relative to their starting point when this happens? 12 table graph (c) rather then looking at clock readings look at the change in time. Also look at the absolute value of the velocity for each car. (graph) The picture shows a ball rolling toward a wall, hits the wall and rolls backward. On the way back it rolls over some felt and slows down. The position marks on the drawing represent 1 meter and the times are 1/5 second. Make a position-time table of the ball s motion. Make a position-time graph of the ball s motion table graph table graph (c) motion map (d) (e) (f) 13 The hare is traveling at 1 m/s while the turtle is traveling at 0.5 m/s. Make a table showing the position of the hair and turtile. stop when the hare catches the turtle. Use 5 second intervals. Draw a motion map to show when the hair catches the turtle. (c) Draw a position time graph of the motion of the hare and the turtle. (d) At what time does the hare catch the turtle? (e) At what position does the hare catch the turtle? table motion map (c) graph (d) 24 seconds (e) 19 meters

4 14 The picture show a motion map of an airplane landing Make a position- time table of the airplane s motion. Make a position-time graph of the airplane s motion. T 1 = 240 T 2 = 150 T 3 = 90 T 4 = 45 T 5 = 7.5 graph 17 The figure shows two ball traveling in the same direction. The first ball is traveling at 2 cm/s and located at the -3 cm mark. The second ball is traveling at 5 cm/s and located at the 4 cm mark. Make sure you indicate the time interval you are using to answer each of the questions below. Make a position time table for each of the two balls. Make a position-time graph for each of the balls. (c) Complete the motion map to show when the second ball catches up with the first ball. (d) At what position does the second ball catch up with the first ball? (e) At what time does the second ball catch up with the first ball? 15 The picture show a motion map of a car traveling in a straight line. Make a position- time table of the car s motion. Make a position-time graph of the car s motion. table graph (c) motion map (d) (e) 18 The picture show a motion map of a car traveling in a straight line. Make a position- time table of the car s motion. Make a position-time graph of the car s motion. table graph 16 The picture show a motion map of a car traveling in a straight line. Make a position- time table of the car s motion. Make a position-time graph of the car s motion. table graph

5 19 The diagram shows three cars traveling south. Car X is moving at 45 mph, Car Y at 35 mph, and Car Z at 30 mph. Assume Car X is 40 miles north of the reference line, Car Y is 20 miles south of the reference line and Car Z is 30 miles south of the reference line Make a position time table for each of the cars. Make a position time graph for each car. Make sure you place all three cars on the same axis. (c) At what time does Car Y catch up with Car Z? (d) What is the path length of Car Y and Car Z when Car Y catches Car Z? (e) At what time does Car X catch up with Car Z? (f) What is the path length of Car X and Car Z when Car X catches up with Car Z? 22 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. Make a table of the sailboat positions at each interval of time. 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? Time X Y Z Graph (c) 2 hours (d) 70 miles, 30 miles (e) 6 hours (f) 270 miles, 90 miles 23 The diagram shows a strobe photograph of the movement of a car at equal intervals of time. Make a table of the car s position at each interval of time. Make a graph of the car s position verses time? What is the cart s displacement during the 8 second interval? (c) What is the cart s path length during the 8 second time interval? 20 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? the duck s displacement must also be zero (c) 21 Does knowing the displacement between the positions of two objects give you enough information to locate the objects? Explain. No, because a single displacement value could correspond to a variety of different positions of the objects. 24 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. The car is shown at 2 s intervals. Note: Each mark on the drawing represents 1 meter Make a table of the car position at each time. Make a graph of the car s position at each time. (c) What is the cart s displacement at 12 seconds (d) What is the path length the car moved at 12 seconds? (c) (d)

6 25 While John is traveling along an interstate highway, he notices a 160-mile marker as he passes through a town. Later John passes another mile marker, 115. What is the distance (path length) between town and John's current location? What is the displacement between town and John s current location? (c) What is John's current position? 30 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. What was the average velocity during the first two hours; What was the average velocity during the first three hours; (c) What was the average velocity during the entire four-hour period? 45 miles assuming that John is traveling in a straight line if not cannot tell from the information. 45 miles (c) km/hr 0.2 km/hr N (c) -1 km/hr 26 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. What is John's displacement from the 260-mile marker? What is Jon's distance from the 260-mile mark? (c) What is the total path length that John traveled? 31 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 m/s) during the entire trip? mi. +85 mi (c) 135 mi. Here are three pairs of initial and final positions, respectively, along an x axis. Which pairs give a negative displacement: -3 m, +5 m -3 m, -7 m (c) +7 m, -3 m m/s 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? 0.98 m/s to the east 28 b and c 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? 33 A bus stop is 0.68 km down he street from the museum and it takes you 9.5 minutes to walk north from the bus stop to the museum entrance. Draw a picture of the situation What is your average speed in m/s? (c) What is your direction? (d) What is your average velocity? 12.5 km/h 3.47 m/s to the south Picture 1.2 m/s (c) North. (d) 1.2 m/s N 29 The Olympic record for the marathon is 2 h, 9 min, 21 s. The marathon distance (path length) is km. Determine the average speed in m/s of a runner achieving this record. 34 El Paso is 1142 km south of Denver. A bus makes the trip from El Paso to Denver in h, What is its average velocity in km/hr? What is its average velocity in m/s? m/s m/s S

7 35 36 You live 10.0 km from your school and the bus takes 0.53 h to reach the school from your house driving due east. Draw a picture of the situation What is the average velocity of the bus in km/hr? What is the average velocity of the bus in m/s? Picture 10 km/hr E (c) 5.3 m/s E During a race on level ground, Andrea covers 825 m in 137 s while running due west. Find Andrea s average velocity. 39 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. The car is shown at 2 s intervals. Note: Each mark on the scale stands for 30 cm. What is the average velocity of the car for the first 4 seconds What is the average velocity of the car from 4 to 8 seconds? (c) What is the average velocity of the car from 8 to 10 seconds? (d) What is the average velocity of the car from 10 to 12 seconds? (e) What is the average velocity of the car from 12 to 14 seconds? (f) What is the average velocity of the car for the entire 14 second run? 6.02 m/s to the west 37 An athlete swims from the north end to the south end of a m pool in 20.0 s and makes the return trip to the starting position in 22.0 s. What is the average velocity for the first half of the swim? 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? 2.50 m/s to the south 2.27 m/s to the north (c) 0.0 m/s (d) 2.38 m/s 40 (c) (d) (e) (f) 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. Which sailboat has the greater average velocity over the first two seconds? Which sailboat has the greater average velocity over the entire 4-second time interval? 38 The figure shows a car s position over a six second run. What is the average velocity of the car for each one-second interval? What is the car s average velocity during the entire six second run? 41 The figure shows a strobe photograph of a ball over a 6 interval time period. Each interval is 1/20 of a second. What is the average velocity of the ball during each time interval? What is the average velocity of the ball for the entire time period shown in the picture?

8 42 The picture show the motion map of a toy car traveling along a straight line. Assume each mark is 10 cm. Make a position time table of the toy car shown in the picture. Make a position time graph of the toy car for the entire time shown. (c) Describe the motion of the car in words. 45 The data in the table gives the position and clock readings of an object moving east during a four second time interval. Use the data to calculate the average velocity during each onesecond interval. (c) 43 The table gives the position and clock readings of an arrow traveling south during a 4.0 second flight. Draw a motion map of the arrow s flight. Use the data in the table to calculate the average velocity for the time interval between 1.5 and 3.0 seconds (c) Use the data in the table to calculate the average velocity for the time interval between 1.0 and 3.0 seconds m/s, 18.9 m/s 51.3 m/s 99.9 m/s Positions (in meters) and times (in seconds) are shown in the table for a moving object. Determine which one-second-time interval corresponds to the greatest velocity. 44 Picture 46 m/sec 48 m/sec The data in the table gives the position and clock readings for an object moving east during a four second time interval. Determine the average velocity of the object between t 1 = 2 s to t 2 = 4 s. Determine the average speed of the object between t 1 = 2 s to t 2 = 4 s sec, 3 sec 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. What his her average speed in km/hr? What is her average speed in m/s? (c) What is her average velocity? 15 km/h 4.17 m/s (c) 0 48 A high-performance jet plane, practicing radar avoidance maneuvers, is in horizontal flight 35 m above the level ground. Suddenly, the plane encounters terrain that slopes gently upward at 4.3 0, an amount difficult to detect. Draw a picture of situation described above How much time does the pilot have to make a correction to avoid flying into the ground? The speed of the plane is 1300 km/h m/sec E 75.6 m/s 1,27 seconds

9 49 A mining cart is pulled up a hill at 20 km/h and then pulled back down the hill at 35 km/h through its original level. (The time required for the cart's reversal at the top of its climb is negligible.) Draw a picture of the situation What is the average speed of the cart for its round trip, from its original level back to its original level? (c) What was the average velocity of the entire trip 54 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. Rank the paths according to the average velocity of the objects, greatest first. Rank the paths according to the average speed of the objects, greatest first. Picture 25 km/h (c) 0 m/s 50 An airplane travels 2400 km at a speed of 800 km/h, and then encounters a tailwind that boosts its speed to 1000 km/h for the next 1800 km. What was the total time (hours) for the trip? What was the average speed in m/s of the plane for this trip? all tie; 4, tie of 1 and 2, then hours m/s 875 km/hr 55 Two locomotives shown in the figure approach each other on parallel tracks. Each has a speed of 120 km/h with respect to the ground. If they are initially 8.5 km apart, how long will it be before they pass each other? 51 During a hard sneeze, your eyes might shut for 0.50 s. If you are driving a car at 90 km/h during such a sneeze, how far does the car move during that time? 12.5 m 127 s 52 On average, an eye blink lasts about 100 ms. How far does a MiG-25 "Foxbat" fighter travel during a pilot's blink if the plane's average velocity is 3400 km/h? 56 When the legal speed limit for the New York Thruway was increased from 55 mi./h (=88.5 km/h) to 65 mi./h (=105 km/h), how much time was saved by a motorist who drove the 435 mi. (=700 km) between the Buffalo entrance and the New York City exit at the legal speed limit? m The 1992 world speed record for a bicycle (human powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling s, at which he commented, "Cogito ergo zoom!" (I think, therefore I go fast!). In 2001, Sam Whittingham beat Huber's record by 19.0 km/h. What was Whittingham's time through the 200 m? 1 hour 13 minutes 1.23 hours.134 km/min s

10 57 You drive on Interstate 10 from San Antonio to Houston, half the time at 35.0 mi./hr (= 56.3 km/h) and the other half at 55.0 mi./h (= 88.5 km/h). On the way back you travel half the distance at 35.0 mi./h and the other half at 55.0 mi./h. What is your average speed from San Antonio to Houston 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) Graph x versus t for, assuming the motion is all in the positive x direction. (f) Describe how the average velocity can be found on the graph 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? 6.5 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 10 2 km/h. If a falcon flies at this speed for 2.00 s and then flies another 1.00 x 10 2 m in 2.50 s, what is the falcon's average speed for the entire flight? mi./h (72.4 km/h) 42.8 mi./h (68.8 km/hr) (c) 43.9 mi./h (70.6 km/h) (d) 0 (e) (f) 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. What is your average speed from San Antonio to Houston? 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, assuming the motion is all in the positive x direction. Indicate how the average velocity can be found on the sketch. 73km/h; 68km/h; (c) 70km/h; (d) km/h 53.1 m/s 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. What is the average velocity for the total trip? What is the displacement for the total trip? 78 km/h to the south 490 km to the south 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. What is the mamba's average speed? What is the mamba's average velocity? 59 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? 128 km/h m/s 0 m/s 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. Determine the average speed for the trip. Determine the average velocity for the trip. (c) Determine the total distance traveled 60 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? 128 km/h km/h 535 km/h (c) 91.0 km 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? 24 s

11 67 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? 71 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? 6.2 s 68 The figure is a graph of a particle's position along an x axis versus time. At time t = 0, what is the sign of the particle's position? 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? meters The table shows the movement of two objects over a 70 minute interval Draw a position time graph of both objects motion. Make sure you put both objects on the same axis. Why is a graph better then a motion map? (c) During which time interval does the maximum displacement occur with object 1. (d) During which time interval does the maximum time interval occur with object 2. (e) During which time interval does the maximum displacement occur with object 1. (f) During which time interval does the maximum time interval occur with object 2. negative; positive; (c) zero; (d) negative; (e) twice 69 The graph of x versus t in the figure is for a particle in straightline motion. State, for each of the intervals AB, BC, CD, and DE, whether the velocity v is positive, negative, or 0 a graph motion too complex (c) 30 to 40 s (d) 30 to 40 s (e) 20 to 30 s (f) 50 to 60 s 73 The picture shows the motion map of a car moving north. Plot the position-time graph of the motion. What does the graph reveal about the motion of the car? (c) Determine the distance traveled by the car at the end of 9 s AB = positive BC = Positive CD = Zero DE = Negative 70 In 1 km races, runner 1 on track 1 (with time 2 min, s) appears to be faster than runner 2 on track 2 (2 min, s). However, length L 2 of track 2 might be slightly greater than length L 1 of track 1. How large can L 2 - L 1 be for us still to conclude that runner 1 is faster? 1.4 m

12 74 The picture shows the motion map of a car moving north. Plot the position-time graph of the motion. What does the graph reveal about the motion of the car? (c) Determine the distance traveled by the car at the end of 30 s 76 Use the figure to answer the following questions? What is the total distance (path length) traveled during the recorded time interval? What is the displacement? 75 The position of an object during a 20-second time interval is shown in the figure What is the object s path length between t = 0 s and t = 5 s. 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 m +5.0 m The picture shows the motion map of a car moving north. Plot the position-time graph of the motion. What does the graph reveal about the motion of the car? (c) Determine the distance (path length) traveled by the car at the end of 9 s (c) 10 m 30 m (c) 0 m (d) 40 m (e) 80 m distance 78 The picture shows the movement of a ball hitting a wall and rebounding backward. The light flashes every 1/2-second. the intervals stand for 0.5 m Plot the position-time graph of the motion. What does the graph reveal about the motion of the ball? (c) Determine the distance (path length) traveled by the car at the end of 20 s. (d) Determine the displacement traveled by the car at the end of 20 seconds. (c) (d)

13 79 The picture shows the movement of a ball. The light flashes every 2-seconds Plot the position-time graph of the motion. What does the graph reveal about the motion of the ball? (c) Determine the distance (path length) traveled by the car at the end of 12 s. 82 The position traveled by an arrow is given in the table. Draw a position time graph Use interpolation and the data in the table to estimate the position of the arrow at t = 0.75 s. (c) 80 The diagram shows a strobe photograph (motion map) of the movement of a car at equal intervals of time. Make a position-time table of the motion of the car. Plot the position-time graph of the motion. (c) What does the graph reveal about the motion of the cart? (d) Determine the distance (path length) traveled by the car at the end of 8th time interval. graph 45 m 83 An object s position in meters and times (in seconds) are recorded in the table. Draw the graph Use (linear) interpolation to obtain the object s position at t = 0.5 s and (c) Use (linear) interpolation to obtain the object s position at t = 2.75 s. table graph (c) (d) 81 The position traveled by a car over a 10-s time interval increased as shown in the table. Plot the position-time graph of the motion. What does the graph reveal about the motion of the car? (c) Determine the distance traveled by the car at the end of 5.5 s graph 0.25 m (c) exact or 8 from graph graph linear constant velocity (c) about 97

14 84 The position of an object during a 20-second time interval is shown in the figure. What is the object s displacement between t = 0 s and t = 5 s. 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 86 The position a steel ball rolls down an incline at the end of each second of travel is given in the table. Draw a position-time graph of the motion of the ball. What type of curve is the line of the graph? (c) What distance (path length) has the ball rolled at the end of 2.2 s? parabola (c) 10 m m 30 m (c) 0 m (d) -40 m (e) 0 displacement The following table gives the total vertical distance a ball is off the ground during each second of flight. Draw a position-time graph of the motion of the ball. How far off the ground is the ball at the end of 0.5 s? (c) When would the ball again be this distance from the ground? 87 The figure is a graph of the position of an object over a given time interval. Use the position-time graph to find how far the object travels between t = 0 s and t = 40 s 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 400 m 0 (c) m Upside down parabola 13.5 m, (c) 5.5 s

15 88 The graph of x versus t in the figure is for a particle in straightline motion. State, for each of the intervals AB, BC, CD, and DE, whether the velocity v is positive, negative, or 0 90 The position of an object over time is shown in the figure. Find the average velocity of an object between t = 10 and 12 s 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 AB = Positive BC = Zero CD = Positive DE = Positive 89 A position-time graph of an object is shown in the figure. Use the position-time graph to find the object's velocity between t = 0 s and t = 5 s. 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 m/s m/s (c) m/s (d) +.4 ms/ The figure is the position-time graph for a squirrel running along a clothesline. What is the squirrel's displacement during the time interval from t = 0.0 s to t = 3.0 s? What is the squirrel's average velocity during this interval? 2 m/s 6 m/s (c) 0 m/s (d) -8 m/s (e) 0 m/s -2.0 m -.67 m/s

16 92 The position traveled by a car over a 10-s time interval increased as shown in the table. Draw a position time graph of the motion of the car. Determine the speed of the car in meters/second (c) Determine the speed of the car in km/hr. 94 A position-time graph of an object is shown in the figure. Use the position-time graph to find the object's velocity between t = 0 s and t = 5 s. 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 graph 17.5 m/s (c) 63 km/hr 93 The position a piece of ice slid down a 7.5-m slope at the end of each second after its release is given in the table. Make a position-time graph of its motion. How far will the ice have traveled at the end of 3.5 s? (c) Determine the speed of the ice at that time from the graph. 2 m/s 6 m/s (c) 0 m/s (d) -8 m/s (e) 0 m/s 95 Two cars are headed in the same direction; one traveling 60 km/h is 20 km ahead of the other traveling 80 km/h. Draw a position-time graph showing the motion of the cars. Use your graph to find the time when the faster car overtakes the slower one. graph 3.6 m (c) 1.9 m/sec 1 h 96 A position time graph for an object is shown in the figure. Obtain the average velocity of the object between 1s and 4s 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 (c)

17 97 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. 99 A position time graph for an object is shown in the figure. Obtain the velocity of the object at 1 s Obtain the velocity of the object at 2 s (c) Obtain the velocity of the object at 4 s m/s m/s m/s m/s m/s m/s m/s m/s m/s m/s m/s -4 m/s (c) m/s An object moves as shown in the graph shown in the figure. Calculate the object's velocity at t = 3 s. 98 A position time graph for an object is shown in the figure. Determine the slope of the object at 1 s Determine the slope of the object at 4 s. -10 m/s 101 On the position-time graph shown in the figure, what represents the velocity? 6.4 m/s 2.4 m/s The slope of the line at each point.

18 102 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. 104 The figures shows position-time graphs of the straight-line movement of two brown bears in wildlife preserve. Which bear has the greater average velocity over the entire period? 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. t 1 ; negative t 2 ; positive t 3 ; positive t 4 ; negative t 5 ; zero 103 Use the position-time graph in the figure to answer the following questions: During which time interval(s) is the magnitude of the velocity (speed) decreasing? During which time interval(s) is the magnitude of the velocity (speed) increasing Bear B Bear A (c) No (d) No 105 A position time graph for an object is shown in the figure. Determine the slope of the object at 2 s Determine the slope of the object at 3 s. 0 to t 1 t 1 to t 2 t 3 to t 4 t 4 to t 5 t 1 to t 2 t 2 to t 3 t 3 to t 4

19 106 A position time graph for an object is shown in the figure. What is the average velocity between 3 s and 5 s? What is the average velocity between 0 s and 4 s? 109 Car A moves at a constant speed while car B has a changing velocity. Find the instantaneous speed of car B at 2.0 s. Find the instantaneous speed of car A at 2.0 s. (c) Find the instantaneous speed of car B at 9.0 s. (d) Find the instantaneous speed of car B at 9.0 s. 7.5 m/s 7.5 m/s 107 For the position time graph shown in the figure, determine the velocity at t = 2 sec. (c) (d) 110 Simpson drives his car with an average velocity of 24 m/s toward the east. He drives 560 km on a perfectly straight highway How much time would Simpson save by increasing his average velocity to 26 m/s east? Sketch a position time graph of his two speeds. 0.5 h graph 108 A ball is thrown straight up into the air. Draw a position-time graph of the ball Calculate the ball s instantaneous velocity at t = 2 s. (c) Calculate the ball s instantaneous velocity at t = 3 s. (d) Calculate the ball s instantaneous velocity at t = 4 s. 111 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. 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? Show how you would solve this problem using a graph. Time Distance (s) (m) km/hr explain 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? app 10 m/s 0 m/s (c) app -10 m/s 2.81 h

20 113 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. Draw a position time graph for both the tortoise and the hair. Put both critters on the same axis. How long does the race take? (c) What is the length of the race? (d) Solve the problem using algebra. 118 Which of the following graphs best matches the data shown to the left? 126 s (c) 1260 cm (d) a 114 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. Make a position time table for the two runners Draw a position time graph for the runners (c) How far are the runners from the flagpole when their paths cross? (d) Solve the problem by algebra. 119 Which of the following equations best matches the data shown to the left? (mass) 2 = 1.29 (volume) (mass) (volume)= 1.29 (c) mass = 1.29 (volume) (d) mass = 1.29 (volume) 2 table graph (c) 0.2 km west of the flagpole (d) algebra solution 115 Ann is driving down a street at 55 km/h. Suddenly a child runs into the street. It takes Ann 0.75 s to react and apply the brakes. Draw a position time graph of the motion How many meters will she have moved before she begins to slow down? 120 c Prepare a graph using the data on the left. Determine an equation that accurately describes the data. graph 11.5 m 116 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. 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? Show how you would solve this problem using a graph. y = 1.5 x 280 km/hr explain 117 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? 2.81 h

21 121 Determine the equation from the graph shown to the left 124 Prepare a graph using the data to the left. Determine an equation that accurately describes the data. 125 What is the general equation of the graph shown to the left? 122 Prepare a graph using the data to the left. Determine an equation that accurately describes the data. V x P = 80,000 or V = 80,000/P 126 What is the general equation of the graph shown to the left? 123 Prepare a graph using the data to the left. Determine an equation that accurately describes the data.

22 127 What is the general equation of the graph shown to the left 130 the questions about the sets of data below. First try answering the question by simply looking at the data. Then prepare a graph of each set and see if the questions are easier to answer. In which graph is y directly proportional to x? In which graph does y decrease as x increases? (c) In which set of data is y inversely proportional to x? (d) Which graph does not seem to picture a simple relationship? (e) Which graph has the general equation y = kx 128 Suppose you recorded the following data during a study of the relationship of force and acceleration. Prepare a graph showing these data. Describe the relationship between force and acceleration as shown by the graph. What is the slope of the graph? Remember to include units with your slope. One newton equals s 1 kg.m/s 2. (c) What physical quantity does the slope represent? (d) Write an equation for the line. (e) What is the value of the force for an acceleration of 15 m/s 2 (f) What is the acceleration when the force is 500 N? 131 Prepare a graph using the data to the left. Determine an equation that accurately describes the data. 132 Prepare a graph using the data to the left. Determine an equation that accurately describes the data. 129 Prepare a graph using the following data. Describe the relationship between x and y and write a general equation for the curve. Is the distance traveled greater between 0 s and 1 s or 3s and 4 s? (c) Is the slope of the curve greater between 1 s and 2 s or 3 s and 4 s? 133 Prepare a graph using the data to the left. Determine an equation that accurately describes the data.

23 134 Prepare a graph using the data to the left. Determine an equation that accurately describes the data. 137 Explain in your own words the significance of a steeper line, or larger slope to the graph of reaction distance versus speed shown to the left: 135 The graph on the left shows a zero y-intercept. What is the meaning of a non-zero y-intercept in the graph of reaction distance versus speed shown below? A steeper line means a longer reaction time. 138 The figure below shows the relationship between the circumference and the diameter of a circle. What is the meaning of the slope of the graph? Could a different straight line describe a different circle? Circumference vs Diameter It would mean that the car moved a non-zero distance when its original speed was zero. Circumference (cm) diameter (cm) 136 In the graph to the left what speed is the reaction distance 10 m? There is only one straight line. The slope is p. between 12 and 13 m/s

24 139 The figure to the left shows the mass of three substances for volumes between 0 and 60 cm 3. What is the mass of 30 cm 3 of each substance (include the uncertainty) If you had 100 g of each substance, what would their volumes be? include the uncertainty) (c) What does the slope represent? (d) Describe the meaning of the steepness of the three lines in this graph (a single word is not a sufficient answer!). 141 During a class demonstration, an instructor placed a 1.0 kg mass on a horizontal table that was nearly frictionless. The instructor then applied various horizontal forces to the mass and measured the rate at which the mass gained speed (was accelerated) for each force applied. The results of the experiment are shown in the table below. Plot the values given in the table and draw the curve that best fits all points. Describe the resulting curve. (c) Describe in words, the relationship between force and acceleration according to the graph (d) Write the equation relating the force and the acceleration that results from the graph (e) Find the units of the slope of the graph Force N Acc m/s 2 80 g 260 g (c) 400g 37 cm3 11 cm3 (c) 7 cm3 (c) The steepness represents the increased mass of each additional cubic centimeter of the substance. (d) Refer to the Problems and Solutions manual linear (c) The acceleration varies directly with the force (d) F = ka or a = kf (e) m/s 2.N 140 During an experiment, a student measured the mass of 10.0 cm 3 of alcohol. The student then measured the mass of 20.0 cm 3 of alcohol. The data is reported in the table below Plot the values given in the table and draw the curve that best fits all points Describe the resulting curve (c) Use the graph to write an equation relating the volume to the mass of alcohol (use V and M instead of x and y) (d) Find the units of the slope of the graph. (e) What is the name given to the slope of this quantity? Volume cm 3 Mass g Refer to the problems and solutions manual a straight line (c) M = mv, where m is the slope (d) mass/volume (e) density 142 During a class demonstration an instructor placed a 1.0 kg mass on a horizontal table that was nearly frictionless. The instructor then varied the mass while the force was held constant. The acceleration on each mass was then recorded. The results are shown in the table below Plot the values given in the table and draw the curve that best fits all points Describe the resulting curve (c) According to the graph, what is the relationship between mass and the acceleration produced by a constant force? (d) Write the equation relating the acceleration to mass given by the data in the graph (e) Find the units of the constant in the equation Mass kg Acc m/s Refer to the Problems and Solutions Manual hyperbola (c) Acceleration varies inversely with the mass (d) a = c/m or a = 12/m (e) kg.m/s 2

25 143 The following data table was established showing the total distances an object fell during various lengths of time. Plot distance vs. time from the values given in the table and draw a curve that best fits all points Describe the resulting curve. (c) According to the graph, what is the relationship between distance and time for a free-falling object? (d) Write the equation relating the distance to the time. (e) Find the units of the constants in the equation. Time (s) Distance (m) Suppose you receive $5.00 at the beginning of a week and spend $1.00 each day for lunch. You prepare a graph of the amount you have left at the end of each day. Would the slope of this graph be positive, zero, or negative? Why? Negative, because the change in vertical distance is negative for a positive change in horizontal distance. Data are plotted on a graph and the value on the y-axis is the same for each value of the independent variable. What is the slope? Why? Zero. The change in vertical distance is zero. 144 Refer to problems and solution manual the curve is parabolic, concave, upward (c) d = 5t 2 (d) d = at 2 + b (e) m/s 2 and m The total distance a lab cart travels during specified lengths of time is given in the following table. Plot distance versus time from the values given in the table and draw the curve that best fits all points. Describe the resulting curve (c) According to the graph, what type of relationship exists between the total distance traveled by the lab cart and the time? (d) What is the slope of this graph? (e) Write an equation relating distance and time for this data. Time (s) Distance (m) A person who has consumed alcohol usually has longer reaction times than a person who has consumed alcohol. Thus, the time between seeing a stoplight and hitting the brakes would be longer for the drinker than for the nondrinker. For a fixed speed, would the "reaction distance for such a driver be longer or shorter than for a non drinking driver? Would the slope of the graph of reaction distance (x-axis) versus speed (y-axis) have a larger or smaller slope? Longer reaction distance because d = vt and t is larger. Larger slope because the vertical distance increases more rapidly with speed. When plotting a graph of an experiment in which the temperature of the gas in a balloon is varied and the resultant volume is measured What quantity is plotted as the abscissa (horizontally)? What quantity is plotted as the ordinate (vertically)? temperature volume Refer to the problems and Solutions Manual straight line (c) linear relationship (d) 0.30 m/s (e) d = 0.30 t 150 A relationship between the independent variable x and the dependent variable y can be written using the equation y = ax 2, where a is a constant. What is the shape of the graph of this equation? If z = x 2, what would be the shape of the graph y = az? (make a table of the function and plot the graph) 145 The graph of braking distance versus car speed is part of a parabola. Thus we write the equation d = kv 2. The distance, d has units meters, and velocity, v, has units meters/second. How could you find the units of k? What would they be? parabolic Linear since y is being plotted versus the square of x, not x Solve for k: kv 2 = d, k = d/v 2 the units of k are m/(m/s) 2 = s 2 /m

26 151 According to the formula F = mv 2 /r what relationship exists between F and r? F and m? (c) F and v? 156 Write an equation that describes the graph shown on the left. inverse relationship direct relationship (c) direct relationship with the square of v 152 According to the formula F = mv 2 /r what type of graph would be drawn for F versus r? F versus m? (c) F versus v? hyperbola straight line (c) parabola 153 How do you find the slope of straight-line or linear graph? The slope of the linear graph is the ratio of the vertical change to the horizontal change, or rise over run. 154 Write an equation that describes the graph shown on the left. 155 Write an equation that describes the graph shown on the left.