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Part One: Motion 2

SECTION 1.1 AN OBJECT IN MOTION CHANGES POSITION. Reading Study Guide A BIG IDEA The motion of an object can be described and predicted. KEY CONCEPT An object in motion changes position. Vocabulary position the location of a place or an object reference point a location to which other locations are compared motion a change of position over time CHAPTER 1 Motion Review 1. Name three directions in which an object can move. Take Notes I. Position describes the location of an object. (p. 9) 2. Describe your position right now in relation to the position of another person, place, or object. Copyright by McDougal Littell, a division of Houghton Mifflin Company A. Describing a Position (p. 10) 3. Why do you need a reference point to describe a location? 4. Describing a position on Earth requires two pieces of information. In the two cases below, one piece of information is given. Fill in the missing piece. Distance Longitude MOTION AND FORCES, CHAPTER 1, READING STUDY GUIDE A 13 3

Activity 1: Running the Race What do you think? o How can you measure a runner s speed? o Does running twice as far take twice as much time? Below, record the time it takes each runner to reach the 5, 10, 15, 20 and 25-meter positions. Calculate the overall average speed for each runner using the equation speed = distance time Runner Name 5m 10 m 15 m 20 m 25 m Average Speed Calculate the amount of time taken to run each 5-m interval. o To calculate the time taken to run from 5-m to 10-m mark, you will need to subtract the time at the 5-m mark from the time at the 10- m mark. o Record your information on the chart below. 0-5 m 5-10 m 10-15 m 15-20 m 20-25 m Speed Speed Speed Speed Speed Speed 5

Calculate the average speed during each 5-m interval. o Record in the shaded part of the chart on the previous page. Remember: Your distance for each interval is 5 meters! Use your data to answer the questions listed below. Answer in complete sentences. 1. In which distance interval did each runner have the greatest average speed? Circle the fastest speed on your chart for each runner. 2. Was the time interval of greatest speed the same or different for different runners? 3. Which runner holds the record for the fastest 5-m interval? 4. Choose one runner and describe that runner s total dash in terms of speed during distance intervals. 5. Estimate the amount of time taken for each runner to reach maximum speed. 6. Write suggestions for the runners to improve their performances. 6

Physics to Go Distance (m) Penn Relays Record Times Time - Men (Minutes:seconds) Time-Women (Minutes:seconds) 100 0:10.47 0:11.44 200 0:21.07 0:23.66 400 0:45.49 0.52.33 800 1:48.8 2:05.4 1500 3:49.67 4:24.0 Mile 4:08.7 4:49.2 3000 8:05.8 9:15.3 5000 15:09.36 16:59.5 1. a. Calculate the average speed of the male who holds the Penn Relays record for the 1500-m run. b. From the data you gathered, are there students in your class who can reach the same speed as the male 1500-m record holder? c. Do you think the fastest student in your class could run the 1500-m in record time? 2. Calculate the average speeds of women who hold Penn Relays records in the 100, 200, 400 and 1500-m runs. What is the pattern of speeds? a. 100m b. 200m c. 400m d. 1500m 7

Activity 1: Speed Problems Use the circle shown at right to calculate the answers to problems #1-4. Include the units for each problem as well. 1. Calculate the speed for a car that went a distance of 125 miles in 2 hours time. S D T 2. A baseball is thrown a distance of 60 meters. What is its speed if it takes 0.5 seconds to cover the distance? 3. How much time does it take a bird flying at a speed of 45 miles per hour to travel a distance of 1,800 miles? 4. A comet is cruising through the solar system at a speed of 50,000 kilometers per hour for 4 hours time. How far did the comet travel during this time? 5. A coach wants to find out the speed of the runners on a track team. What simple equipment does the coach need in order to do this? How should it be done? - Equipment Needed: - What should be done: 8

Activity 2: Analysis of Trends What do you think? o Current trends indicate that women will start outrunning men in 65 years. Is it useful to compare track records over many years of time? Can future track records be predicted based on past performances? Part One Look at the graph below, Speed Versus Year: Men s Olympic 400-m Dash o The average speed of runners is shown on the vertical axis, and the year in which the race was run is shown on the horizontal axis. o Take a moment to be sure you understand that the plotted points shows a 100-year history of the speeds of male athletes in the Olympic 400-m dash. Sketch either a straight line or a smooth, curved line through the data points to show what you think is the shape of the graph. What do you see as the trend of average speed in the 400-m dash over the past 100 years? 9

Make the best guess you can to sketch how the graph would continue to the year 2020. This process of going beyond the data is called extrapolation. Try it. According to your extrapolation, what will be the speed of the winning runner in the men s Olympic 400-m dash in the year 2020? Part Two Look at the graph below, Speed Versus Distance: Men and Women, Penn Relays o The average speed of runners is shown on the vertical axis, and the distance of the race was run is shown on the horizontal axis. o Make sure you understand that there are two sets of plotted points, one for men and one for women. o The points show how average speed varies with distance of the race for both men and women. Sketch the shapes of the graphs for men and women by connecting the plotted points with either a straight line or a smooth, curved line. What do you see as the trend of average speed for both men and women as the distance of the race gets longer and longer? 10

Extropolate from the graphs to predict what the record speed at the Penn Relays would be for the 10,000-m races for both men and women. Try to use extrapolation to find a race distance for which men and women would run at the same average speed. Comment on your attempt. Physics to Go 1. A runner had an average speed of 10.14 m/s for 9.86 s. Calculate the distance the runner traveled. 2. The table below gives the years and the winning times for the women s 400-m dash in the Olympics. Women s 400-m Olympic Dash Year Time (Seconds) Speed (m/s) 1964 52.00 1968 52.00 1972 51.08 1976 49.29 1980 48.88 1984 48.83 1988 48.65 1992 48.83 1996 48.25 2000 49.11 2004 49.41 2008 49.62 a. Calculate the winning speeds in the right column. b. Plot a speed vs. year graph for the data in the given area on the next page. 11

c. What is the trend of the average speeds over the past years? d. From your graph, extrapolate what will be the winning speed in 2020. 12

Activity 2: Speed Practice Problems Use the formula for speed to help you answer the questions on this page. Make sure to show your work! 1. What is the average speed of a car that travels 200 km in 4 hours? 2. What is the average speed of a bus that travels 300 m in 4 seconds? 3. What is the distance traveled if a car had an average speed of 50 km/h for 3 hours? 4. What is the distance traveled if an airplane had an average speed of 160 m/min for 20 minutes? 5. Complete the following chart. Be sure to write out the units for each speed. Distance Time Speed 10 meters 1 second 40 meters 2 seconds 75 millimeters 3 seconds 5 kilometers 10 hours 25 centimeters 100 seconds 75 meters 100 hours 18 centimeters 36 seconds 10 centimeters 0.5 seconds 50 millimeters 0.5 seconds 13

6. Complete the following chart. Be sure to write out the units for each time. Distance Time Speed 33 meters 11 m/sec 45 centimeters 15 cm/hour 100 kilometers 3 km/minute 25 meters 50 m/minute 75 centimeters 25 cm/sec 121 meters 11 m/hour 6 meters 0.5 m/sec 0.5 meters 1 m/sec 14

Activity 2.5: Just Strolling Along What do you think? o How can you measure distance using a stopwatch? o Can you walk at a constant speed? 1. Time yourself as you walk a measured distance three times to see if there is any consistency in your walking. 2. Record the distance that you walked and all the times that you measured while walking the given distance. 3. Next, calculate your average speed. Distance (m) Time (s) Speed (m/s) 4. Calculate your average speed for all trials: 5. Now that you have calculated your average speed, use this value to calculate the distance between two points given to you by your teacher. You may use a stopwatch to measure the time it takes to walk from one point to the other. Time (s) Speed (m/s) **from above** Mystery Distance Average Mystery Distance 15

Activity 3: Who Wins the Race? What do you think? o Who wins the race? The runner with the highest finishing speed? The runner with the highest average speed? The runner with the greatest top speed? PART ONE: Flat Track - Constant Speed In table groups: o Thread a piece of tape about 1 m long in the timer, and attach one end to the car. o Turn on the timer, and pull the car at a nearly constant speed so that the tape is dragged completely through the timer. o Cut the tape so that it only shows the dots (no empty space) Find average speed: o Count the number of ticks (one tick is the distance between two dots) o Average speed is cm divided by the number of ticks. Average Speed = cm/tick Find top speed: o The one (1) tick where the car was traveling the fastest. Using the area where the car was traveling the fastest. Use the one (1) tick where there is the most distance between the dots. Top Speed = cm/tick Find final speed: o The speed at the end of the race. Using the area at the end of the tape usually the last 3 or 4 ticks. Distance in centimeters / number of ticks Final Speed = cm/tick 16

PART TWO: Flat Track - Acceleration In table groups: o Thread a piece of tape about 1 m long in the timer, and attach one end to the car. o Turn on the timer, and push the car down the track so it is accelerating. Make sure the tape is dragged completely through the timer. o Cut the tape so that it only shows the dots (no empty space) Find average speed: Average Speed = cm/tick Find top speed: Top Speed = cm/tick Find final speed: Final Speed = cm/tick PART THREE: Elevated Track In table groups: o Elevate the track by putting some books underneath one end. o Thread a piece of tape about 1 m long in the timer, and attach one end to the car. o Turn on the timer, and let gravity pull the car until the tape is dragged completely through the timer. o Cut the tape so that it only shows the dots (no empty space) Find average speed: Average Speed = cm/tick Find top speed: Top Speed = cm/tick Find final speed: Final Speed = cm/tick 17

Physics to Go 1. A. Is average speed the same as actual speed at every point? B. Does gravity make the car go at a constant speed or an accelerated speed? 2. What would the spacing of dots look like for a ticker tape timer record of an object that is slowing down in its motion? 3. From what you observed and measured during this activity, describe how the speed of a toy car behaves as it travels: a. On a straight ramp that slopes downward: b. On a level surface when the car already has some speed at the beginning: c. On a straight ramp that slopes upward: 4. Aisha and Bert are running at constant speeds, Aisha at 9.0 m/s and Bert at 8.5 m/s. They both cross a starting line at the same time. The finish line is 100 m away. a. How long does it take Aisha to finish the race? b. How long does it take Bert to finish the race? c. Where is Bert when Aisha crosses the finish line? d. By how many meters does Aisha finish ahead of Bert? 18

Ticker Tape Diagrams http://www.physicsclassroom.com/class/1dkin/u1l2b.cfm home - about - terms - credits - feedback» The Physics Classroom» Physics Tutorial» One Dimensional Kinematics 1-D Kinematics - Lesson 2 Describing Motion with Diagrams Physics Tutorial 1-D Kinematics Newton's Laws Vectors - Motion and Forces in Two Dimensions Momentum and Its Conservation Work, Energy, and Power Circular Motion and Satellite Motion Thermal Physics Static Electricity Current Electricity Waves Sound Waves and Music Light Waves and Color Reflection and Ray Model of Light Refraction and Ray Model of Light Minds on Physics The Calculator Pad Multimedia Studios Shockwave Studios The Review Session Physics Help Curriculum Corner The Laboratory The Photo Gallery Ticker Tape Diagrams Introduction Ticker Tape Diagrams Vector Diagrams Student Extras A common way of analyzing the motion of objects in physics Teacher's Guide labs is to perform a ticker tape analysis. A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time - say every 0.10 second. As the object moves, it drags the tape through the "ticker," thus leaving a trail of dots. The trail of dots provides a history of the object's motion and therefore a representation of the object's motion. The distance between dots on a ticker tape represents the object's position change during that time interval. A large distance between dots indicates that the object was moving fast during that time interval. A small distance between dots means the object was moving slow during that time interval. Ticker tapes for a fast- and slow-moving object are depicted below. The analysis of a ticker tape diagram will also reveal if the object is moving with a constant velocity or accelerating. A changing distance between dots indicates a changing velocity and thus an acceleration. A constant distance between dots represents a constant velocity and therefore no acceleration. Ticker tapes for objects moving with a constant velocity and with an accelerated motion are shown below. 1 of 2 11/15/11 12:03 PM 19

Activity 3: Ticker Tape Practice These ticker tapes are of carts rolling along a track. In each case describe the motion of the cart with a complete sentence or two. Does the cart speed up, slow down, or move at a constant speed? 21

11. Which one(s) show the cart moving at a constant speed? 12. Which one(s) show the cart speeding up the whole time? 13. Which one(s) could be of a cart going downhill the whole time? 14. Which one(s) could be of a cart going downhill and then along a level track? 15. Which one(s) could be of a cart going uphill the whole time? 16. Which one(s) shows the cart speeding up during part of its trip? 17. Which one(s) shows the cart slowing down during part of its trip? 18. Which one shows the fastest speed during any part of its trip? 19. Which one shows the fastest initial speed? 20. Which one shows the fastest final speed? 21. Which one is going the slowest at the end of its trip? 22

Ticker Tape Patterns Analysis Activity Use your knowledge about ticker timer tape patterns to help you analyze the ticker tape examples below. Review Ticker Tape Examples. 1. Describe the motion involved by the object that left the following ticker tape patterns. a. b. c. Find the average speed and final speed of: a. Cart A: b. Cart B: 2. Ticker tape diagrams are sometimes referred to as oil drop diagrams. Imagine a car with a leaky engine that drips oil at a regular rate. As the car travels through town, it would leave a trace of oil on the street. That oil trace would reveal information about the motion of the car. Explain the action of the car at each interval. a. b. c. d. Which cart had the greatest top speed? e. Calculate this greatest top speed in cm/tick. 23

3. Draw a diagram of what the ticker tape might look like for the following examples. a. A driver on a two-lane highway is traveling the speed limit when it comes up behind a tractor pulling a large load of hay bales. It follows the tractor for a short distance until oncoming traffic has dissipated, then it pulls out and passes it. After it has passed the tractor it resumes traveling at the speed limit. b. A driver is in a small town where there is a lot of pedestrian traffic. He drives the speed limit and slows to a stop at the stop sign. After stopping, he begins to drive for a half a block, when a small child runs out from behind a parked car. The driver brakes hard and stops, just in time. After the child is safely on the sidewalk, the driver resumes his trip. A half a block away, he sees that a group of young people are crossing the street and slows down. The young people get across the street before he gets too close. He turns at the next corner and into his driveway. c. A roller coaster starts at a high point. As the roller coaster leaves the dock it drops rapidly for thirty seconds before climbing to the very highest point of the ride. As it leaves the top point it drops and rises over three smaller hills before finishing the rest of the ride. 24

SECTION 1.2 SPEED MEASURES HOW FAST POSITION CHANGES. Reading Study Guide A CHAPTER 1 Motion BIG IDEA The motion of an object can be described and predicted. KEY CONCEPT Speed measures how fast position changes. Vocabulary speed a measure of how fast something moves velocity a speed in a specific direction vector a quantity that has both size and direction Review 1. What type of information should be included when describing an object s location from a reference point? You should note the object s and from the reference point. Take Notes I. Position can change at different rates. (p. 16) 2. To measure speed, you need to know distance and. 3. Fill in the diagram to show how two objects with different speeds move in the same amount of time. more speed less speed A. Calculating Speed (p. 17) distance distance in the same time Use the formula for calculating speed (S d ) to answer questions 4 and 5. t 4. What do each of the variables (letters) stand for? 5. If you travel 80 m in 40 s, what is your speed? Copyright by McDougal Littell, a division of Houghton Mifflin Company 24 MOTION AND FORCES, CHAPTER 1, READING STUDY GUIDE A 25

CHAPTER 1 MOTION Math Practice Speed and Distance-Time Graphs Solve the equations to find the value for each question. Include the appropriate units in your answer. CHAPTER 1 Motion 1. S 600 m / 15 s 2. S 240 km / 4 hr 3. S 75 mi / 2.5 hr 4. S (35 m 20 m) / (10 s 5 s) 5. S (46 m 18 m) / (10 s 3 s) 6. S (49 m 21 m) / (14 s 7 s) Use the graph or the formula for speed to answer questions 7 12. Copyright by McDougal Littell, a division of Houghton Mifflin Company 7. A trucker made a delivery to a town 180 km from his start point. The graph shows the time and distance for the trip. During which part of the trip was the trucker driving 55 km/h? 8. The trucker stopped at a truck stop for a one-hour lunch break. During which part of the trip did he take his lunch break? 9. What was the trucker s speed as he drove from the truck stop where he had lunch to his final destination? Distance (km) 180 160 140 120 100 80 60 40 20 Distance-Time Record for Trip A 0 0 1 2 3 4 Time (hours) 10. A jogger runs along a road for a distance of 2700 m. If it takes her 900 seconds to run that distance, what is her speed? 11. A car travels 40 miles in the first hour and 50 miles in the second hour. What is the car s average speed over the entire trip? 5 12. A bicyclist travels 10 km in half an hour, then rests for half an hour, then travels 50 km in three hours. What was the bicyclist s average speed over the entire trip? MOTION AND FORCES, CHAPTER 1, MATH PRACTICE 51 27

CHAPTER 1 MOTION Math Support CHAPTER 1 Motion Speed and Distance-Time Graphs The formula for speed is S d t S is the speed of the object, d is the distance the object has moved, and t is the time it took the object to move that distance. If information about distance and time is presented in a graph form, you can find the speed using the distance and time information given in the graph. Sometimes this involves subtracting one distance from another and subtracting one time from another. SAMPLE PROBLEM Distance (meters) 120 100 80 60 40 distance 120 m 90 m Using the graph above, find the bicyclist s speed between 40 s and 50 s. Use the graph to find the distance at 50 s: 120 m. Use the graph to find the distance at 40 s: 90 m. Find the time interval between 40 s and 50 s: 50 s 40 s 10 s. A Cyclist's Speed 20 time 50s 40s 0 0 10 20 30 40 50 Time (seconds) Find the distance traveled between 40 s and 50 s: 120 m 90 m 30 m. Substitute the distance and the time into the formula for speed: Answer: S d t 3 m 10 s 3 m/s Between 40 s and 50 s, the bicyclist s speed was 3 m/s. EXERCISES... 1. Using the graph above, find the bicyclist s speed between 10 s and 30 s. Find distances from graph. Calculate time interval. Calculate distance traveled. Substitute and solve. 2. Using the graph above, find the bicyclist s speed between 30 s and 40 s. Find distances from graph. Calculate time interval. Calculate distance traveled. Substitute and solve. Copyright by McDougal Littell, a division of Houghton Mifflin Company Answer. Answer. 50 MOTION AND FORCES, CHAPTER 1, MATH SUPPORT 28

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Activity 3.5: PASCO Motion Sensors What do you think? o How would you use your body to re-create the following motion graph? Use some scientific terminology in your response. 100 50 Motion 0 Motion Motion Sensors For each of the following graphs: o Predict the type of motion needed to re-create the graph. o Re-create the graph and describe the motion used. Prediction #1: Description of Motion: 32

Prediction #2: Description of Motion: Prediction #3: Description of Motion: 33

Prediction #4: Description of Motion: ** Now for fun, try to create some numbers, names or appropriate words!!** 34

Distance/Time Graph Practice Problems Examine this graph carefully to answer questions 1 and 2. 1. How far is the truck from its starting point after: (a) 10 s (b) 15 s (c) 30 s (d) 40 s (e) 50 s 2. Under each graph, describe briefly the kind of motion that is taking place in each of the situations represented by the following distance vs. time graphs. a) b) c) 3. 35

3. Under each graph, describe briefly the motions represented by each of these graphs. If the speed is changing, state whether it is increasing or decreasing. a) b) c) Use the following graph for question 4. 4. a) From the graph above, calculate the average speed for the entire 45 m. b) Find the average speed for each of the following time intervals: 0 m to 15 m 15 m to 35 m 35 m to 45 m 36

Activity 4: Understanding the Sprint What do you think? o It was not believed to be humanly possible to run a mile in less than four minutes until Roger Bannister of England did it in 1954. How much time does it take to get up to speed? For You To Do: PART ONE o Carl Lewis established a world record for the 100-m dash at the World Track and Field Championship held in Tokyo, Japan in 1991. The times at which he reached various distances in the race (his split times ) are shown in the table below: Distance (m) 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 Time (s) 0.00 1.88 2.96 3.88 4.77 5.61 6.45 7.29 8.13 9.00 9.86 Complete the table below using Lewis split times. o Use subtraction to calculate the time taken by Carl Lewis to run each 10 m of distance during the race. o Then, calculate Lewis average speed during each 10 m of the race. Distance (m) Time (s) Average Speed (m/s) 0.0-10.0 1.88 5.32 10.0-20.0 20.0-30.0 30.0-40.0 40.0-50.0 50.0-60.0 60.0-70.0 70.0-80.0 80.0-90.0 90.0-100.0 37

PART TWO Use the data you created for the above table to make a bar graph to give you a visual display of Carl Lewis average speed during each 10 m of his world record 100-m dash. Carl Lewis' World Record 100-m Dash Average Speed, 10-m Interval Average Speed (m/s) 12 10 11 9 8 7 6 5 4 3 2 1 0 0-10 10-20 m 20-30 m 30-40 m 40-50 m 50-60 m 60-70 m 70-80 m 80-90 m 90-100 m Distance (m) Analyze the bar graph to answer these questions: 1. At what position in the dash did Lewis reach top speed? 2. How well did Carl Lewis keep his top speed once he reached it? 3. Did he seem to be getting tired at the end of the race? Give evidence. 4. Can you tell how fast Lewis was going at an exact position in the race, such as 15.0 m or 20.0 m? Why or why not? 38

PART THREE Use the splits given at the start of this activity to plot a graph of Carl Lewis position versus time. Plot each position at the appropriate time and connect points to show what you think is the shape of the graph. Carl Lewis' World Record for the 100- m Distance vs. Time Distance (m) 110 100 90 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 Time (sec) PART FOUR Compare the two graphs and answer the following questions: 1. When the line graph is curving early in the run, do the bars on the bar graph change in height or are they fairly steady in height? 2. What does this comparison mean? 3. When the line graph is climbing in a straight line, what is happening to the heights of the bars on the bar graph? 4. What does this comparison mean? 39

Activity 4.5: Interpreting Motion Graphs What do you think? o If you were to measure the speed of a car rolling down a track, do you think the car was going the same speed the whole time? For You To Do: 1. Cut apart the 8 trip strips along the dotted lines. 2. Read the trip strips. Each strip represents a story or one or more pieces of a story. Some of the strips describe Teasha s trip to school. The others describe Josh s trip. 3. With your partner, identify the strip that matches each segment of the two motion graphs below. 4. Place each strip onto the segment of the graph that describes it. 41

Analysis 1. Identify a place on each graph where the slope of the line changes. What does a change in the slope of a motion graph indicate? 2. Which student Teasha or Josh started out faster? Explain how you know this. 3. How far into the trip did Josh turn around? Describe what the graph looks like at this point in the trip. 4. Look at the motion graphs shown below. Match the descriptions here to the correct graphs: a. A car moving at a constant speed stops and then moves in the opposite direction at the same speed. b. A car moving at a constant speed stops and then moves faster in the same direction. c. A car moving at a constant speed changes to a higher constant speed. d. A car moving at a constant speed changes to a lower constant speed. 42

5. A car that accelerates is one that speeds up, slows down, or changes direction. Which graph below shows a car continually accelerating? Explain how the shape of the graph shape shows this. 43

Activity 5: Acceleration What do you think? Your mom is driving you to school with a cup of her favorite Wawa coffee resting level in the cup holder. Describe the action of the coffee (if any) as she: o Suddenly brakes at a red light o Presses the accelerator as the light again turns green. What does it mean to accelerate? For You To Do: In this activity, you will use an accelerometer, a device for measuring acceleration. Look at the accelerometer and then answer the following questions in complete sentences: o Can you get the liquid in the accelerometer to slant one way or the other while keeping the accelerometer level? o What do you need to do to get the liquid to slant? PART ONE Trial 1: Normal Speed (Low Acceleration) Record the observations of the accelerometer as you are completing each movement listed below. For each one, you should: o Describe the height and direction the water moves in each of the each situation. Example: While walking forward from a resting position there is a slow lean in the water in a forward direction, o Draw a picture of what happened. Standing still Walking forward from a resting position and speed up a little. 44

Walk at a fairly constant speed Walking at a constant speed and then slow down to a stop. Trial 2: Faster Speed Record the observations of the accelerometer as you did above for each of the following movements: Start from a resting position faster and speed up faster (fast acceleration) Walk faster at a fairly constant speed and then slow down to a stop faster. (fast stop) Trial 3: Backwards Record the observations of the accelerometer as you did above for each of the following movements: Accelerating while going backward. Stopping while going backward. 45

Analysis Someone said, Deceleration while walking forward is the same as acceleration while walking backward. o Do you agree or disagree? o Use your observations of the accelerometer for your answer. PART TWO: 1. Your teacher will set up an accelerometer that will be pulled by a falling weight. Observe the system and answer the following questions: a. Does the cart appear to accelerate? b. How does the accelerometer show you that it s accelerating? c. Does the accelerometer show that the acceleration is constant or changing? d. How can you tell? 2. Which produced a steadier, constant acceleration: using the falling weights or walking with the accelerometer? 3. What evidence do you have for your answer? 46

Physics to Go 1. Is there anything in nature that has constant acceleration? 2. If Carl Lewis were to carry an accelerometer during the start of a sprint, describe what the accelerometer would do? 3. Did Carl Lewis accelerate for the entire 100 m of his world-record dash? Explain his pattern of acceleration. 4. If you are running, getting tired, and slowing down, are you accelerating? Explain your answer. 47

SECTION 1.3 ACCELERATION MEASURES HOW FAST VELOCITY CHANGES. Reading Study Guide A BIG IDEA The motion of an object can be described and predicted. KEY CONCEPT Acceleration measures how fast velocity changes. Vocabulary acceleration the rate at which velocity changes over time CHAPTER 1 Motion Review 1. Sam said he is walking north at a rate of 5 meters per second. Did he describe his speed or his velocity? Take Notes I. Speed and direction can change with time. (p. 25) 2. Complete the supporting main-idea chart for acceleration. Acceleration Copyright by McDougal Littell, a division of Houghton Mifflin Company measures how quickly and are changing speed of an object increases when acceleration speed of an object decreases when acceleration II. Acceleration can be calculated from velocity and time. (p. 27) 3. In order to measure acceleration, what two things must you know? A. Calculating Acceleration (p. 28) 4. Fill in the words in the formula for acceleration. The first letter is given for each word. a f v i v (divided by) t MOTION AND FORCES, CHAPTER 1, READING STUDY GUIDE A 35 49

Velocity and Acceleration Calculation Practice Acceleration = final velocity - starting velocity = m or km time s 2 h 2 velocity = distance = m or km time s h SHOW YOUR WORK by writing the substitution of the numbers for the letters in the formula. Always include the units in the formula. 1. Starting Velocity = 0 m/s Final Velocity = 30 m/s Time = 10 s Acceleration = 2. Starting Velocity = 100 m/s Final Velocity = 60 m/s Time = 15 s Acceleration = Is this acceleration or deceleration? (circle one) 3. Starting Velocity = 15 km/h Final Velocity = 0 km/h Time =.3 h Acceleration = Is this acceleration or deceleration? (circle one) 4. Starting Velocity = 6 km/h Final Velocity = 75 km/h Time =.25 h Acceleration = Is this acceleration or deceleration? (circle one) Is this acceleration or deceleration? (circle one) 51

5. In steamy South America in the cliffs of the Andes mountains, you are 007 in hot pursuit of the bad guy traveling 1.5 km in 30 seconds (0.0083 hours). What s your speed in km/h? Is this a velocity or acceleration problem? (circle one) Circle the parts of the question that you ll use to solve the problem. What are your final units going to be? Solve: Answer: 6. You see the curve ahead sign and wonder, Am I going too fast? Suddenly, you see the bad guy s car skid out of control going from 160 km/h to 100 km/h in 2 seconds (0.0005 hours)!! What s the bad guy s deceleration? Is this a velocity or acceleration problem? (circle one) Circle the parts of the question that you ll use to solve the problem. What are your final units going to be? Solve:

Acceleration Practice Problems Complete the following acceleration problems using the following formula: Final Velocity Initial Velocity Time SHOW YOUR WORK! 1. At a drag race, the light turns green and 0.00125 hours later, a dragster is traveling 300 miles per hour. Calculate the acceleration of the dragster. 2. An object traveling 200 feet per second slows to 50 feet per second in 5 seconds. Calculate the acceleration of the object. 3. A car going 22 m/s accelerates to pass a truck. Five seconds later the car is going 35 m/s. Calculate the acceleration of the car. 4. Quinn accelerates her skateboard along a straight path from 0 m/s to 4.0 m/s in 2.5 seconds. Calculate the acceleration of the skateboard. 5. Find the average acceleration of a northbound subway train that slows down from 12 m/s to 9.6 m/s in 0.8 seconds. 6. Elyse is traveling east on a dirt road when she spots a pothole ahead. She slows her car from 14.0 m/s to 5.0 m/s in 6.0 seconds. What is the car s acceleration? 7. Lillie is running. She increases her initial speed of 30 km/h to 40 km/h so she can win the race. If she takes 0.05 hours to complete this increase, what is her acceleration? 53

CHAPTER 1 MOTION Math Support CHAPTER 1 Motion Calculating Acceleration Use the formula below when you calculate acceleration. v a final Recall that a is the acceleration, t is the time interval during which the velocity changes, v fi nal is the velocity the object has at the end of the time interval, and v initial is the velocity the object had at the beginning of the time interval. v t initial SAMPLE PROBLEM A soccer ball has a speed of 4 m/s. After 10 seconds, it rolls to a stop. What is the acceleration of the ball? What do you know? v initial 4 m/s v final 0 m/s t 10 s Sometimes you may need to interpret a question to determine some of the information. For example, the phrase rolls to a stop means that the object has a final velocity of 0 m/s. Substitute. a 0m/s 4m/s 10 s Solve. m/s a 10 s 4 2 04. m/s When you have an answer, consider if it makes sense. The ball is slowing down, so the acceleration should be negative. Answer. The soccer ball has an acceleration of 0.4 m/s 2. EXERCISES... 1. A bicyclist initially at rest increases her speed to 6 m/s in 30 seconds. What is her acceleration? Formula Substitute. Solve. 2. A car has an initial velocity of 25 m/s and 3 s later has a velocity of 49 m/s. What is the car s acceleration? Formula Substitute. Solve. Copyright by McDougal Littell, a division of Houghton Mifflin Company Answer. Answer. 52 MOTION AND FORCES, CHAPTER 1, MATH SUPPORT 54

Activity 6: Running a Smart Race What do you think? Good sprinters are usually not good distance runners. o How do strategies for winning sprints and distance runs differ? For You To Do: Assume you are running a 1500-m race that requires four laps around an oval track. You usually run this race at a constant speed in a time of 4 minutes (240 seconds). o Calculate and record the distance of each lap of the race. o Calculate and record the time it takes you to run one lap. o Record how you think you can develop a strategy to win the race. Assume you are running against two opponents, one who starts fast (a rabbit ) and another who finishes fast (a kicker ). You have studied their split times from earlier track meets. From their splits, you have discovered that both runners, like you, usually run the 1500-m in 4 minutes. But there are differences: o The kicker runs the final lap in 58 seconds. o The rabbit runs the final lap in 63 seconds. Calculate the speed of each runner during the final lap of the race in m/s. (Remember speed = distance/time) o Kicker o Rabbit o You 55

Make a graph of distance versus time for the three runners for the final lap of the race. o Scale distance vertically from 0 to 375 m and scale time horizontally from 0 to 63. o Assume that all runners are at d=0 when t=0 and that all runners keep a constant speed during the final lap. o Use the individual times to plot a line on the graph for each runner. o Label the lines. Attach Graph Here 56

Analysis Questions 1. Look at the distance versus time graph. The graph shows that all three runners are even (375 m remaining to run) at the beginning of the final lap. a. In what order will the runners finish the race? b. By how much time will the winner finish ahead of the second-place runner? The third-place runner? c. By how much distance will the winner finish ahead of the secondplace runner? The third-place runner? *Hint: Speed x time = distance 2. You run the final lap in 60 seconds. During those 60 seconds, how far will the rabbit and the kicker travel at the speeds calculated above? **Remember that distance = speed * time 3. How far behind the rabbit can you be at the beginning of the final lap to win the race? 4. How far ahead of the kicker must you be at the beginning of the final lap to win the race? 57

Activity 7: Increasing Top Speed What do you think? A cheetah can reach a top speed of 60 miles per hour (about 30 m/s). o What can a runner do to increase top speed? For You To Do: 1. Watch the video of the runner. Use the total distance traveled and the total time to calculate the runner s speed in yards per second. Speed(m/second) = distance (meters) time (seconds) 2. Find Stride Frequency a. Count the number of strides taken by the runner during the entire run. b. Use the number of strides and the total time to calculate the runner s stride frequency in strides per second. Stride frequency (strides/second) = Number of strides Time (s) 3. Find Stride Length a. Calculate the average length of one stride for the runner. b. To do so, measure the length of several single strides and calculate the average length per stride. c. The unit for your answer will be m/stride. Stride Length = distance / # strides 4. Calculate the speed of each runner using stride length & stride frequency. a. Your answer will be in m/second. Speed = Stride Frequency x Stride Length 58

5. Compare the results of using the two equations calculating speed. a. You calculated speed using two different equations. Did your two answers agree? b. How good is the agreement? c. How would you explain any difference in results? Your Turn: 1. You will test the new equation on a 12-meter track. 2. Marks have been placed at.75-meter intervals. a. Starting from the zero mark, walk so that you step on each mark. b. Count the number of strides to complete the walk, and use a stopwatch to measure the total time. Intervals of.75 m on a 12- m track Your time seconds # of Strides Calculate speed using distance/time. Calculate your stride frequency: o Stride frequency (strides/second) = Number of Strides Time (seconds) Calculate your speed using the stride frequency and stride length (.75 m). o Speed = Stride Frequency x Stride Length 59

What do you think happens to your speed if you change your stride length? o Increase stride length: o Decrease stride length: Test Your Hypothesis: Your time seconds # of Strides Intervals of.50 m on a 12- m track Calculate speed using distance/time. Calculate your stride frequency: o Stride frequency (strides/second) = Number of Strides Time (seconds) Calculate your speed using the stride frequency and stride length (.50 m). o Speed = Stride Frequency x Stride Length Comparison: On the.50 meter interval track, you calculated speed two different ways. How well do your speeds calculated by both methods on this track compare? 60

Compare your performances on the two different tracks. o Was your speed on the track that had 0.75 m stride lengths about the same as, different from, your speed on the track, which had 0.50 m intervals? Why? o If you must step on each mark, what would you need to do to make your speed on the second track equal to your speed on the first track? Physics To Go: 1. A runner s stride length is 2.0 m and her frequency is 1.8 strides/s. o Calculate her average speed. o What would be her time for a 200-m race? 2. A runner maintains a constant speed of 6.0 m/s. If his stride length is 1.5 m, what is his stride frequency? 3. If the runner in Question 2 increases his stride length to 1.6 m without changing his stride frequency, what will be his new speed? 4. If a marching band has a frequency of 2.0 strides/s and if each stride length is 0.65 m, what is the band s marching speed? 61

Activity 8: Projectile Motion What do you think? What is the path of a ball that rolls off the table and falls to the floor? Do you think the speed a ball is going has any bearing on the time it takes to drop from the table to the floor? For You To Do: Set up a ramp by placing books or blocks at the end of the aluminum track so that the other end of the ramp is a few inches before the edge of the table. From the desired position on the track, roll a tennis ball down the ramp so that it rolls off the table and strikes the floor. On the chart below: o Sketch the path taken by the ball from the end of the table until it reaches the floor. o Use a stopwatch to time the ball from when it leaves the edge of the table until it strikes the floor. Record the times and calculate the average time. o Mark where the ball strikes the floor, then measure the distance. 1/3 of way up track 2/3 of way up track All the way up track Sketch of Path: Sketch of Path: Sketch of Path: Average Time (s): Average Time (s): Average Time (s): Distance from Table (cm): Distance from Table (cm): Distance from Table (cm): Speed of the Ball (cm/s) Speed of the Ball (cm/s) Speed of the Ball (cm/s) 62

Analysis: How does the release point of the ball affect the speed of the ball? How does the speed affect the amount of time it takes for the ball to fall from the edge of the table to the floor? (Compare all three runs) How does the release point of the ball affect how far from the table the ball strikes the floor? 63

Activity 8.5: Gravity Measuring g Objective: To find the acceleration of an object in freefall. Materials: Ball, stopwatch, calculator Background: This experiment will use very basic equipment to measure an important quantity, the acceleration of an object in freefall. This is also known as the acceleration due to gravity, or g. The acceleration due to gravity is nearly the same at all points on the earth s surface, or about 10 m/s. You will compare your result to this accepted value. Procedure: 1. Choose one person to be a ball dropper. a. This person will drop a ball from the top of the bleachers. They will have their arm straight out on the top railing of the bleachers and drop the ball straight down. 2. Choose another person to be the timer. 3. Choose a third person to be the recorder. 4. Drop the ball from the designated height ten (10) times and record the time in the chart below. a. Be sure to time exactly from when the ball is released to when it strikes the ground. Trial 1 2 3 4 5 6 7 8 9 10 Drop Distance (m) Time (s) 5. Find the average time. seconds 64

6. When an object moves with constant acceleration from rest, it s distance can be found by using the following equation: d= 1 2 g t2 Manipulate this equation and solve for g g = 2d t 2 65

Acceleration Due to Gravity Calculations 1. Solve for Velocity using V = G x T a. A penny dropped into a wishing well reaches the bottom in 1.50 seconds. What was the velocity at impact? b. In a bizarre but harmless accident, Superman fell from the top of the Eiffel Tower. How fast was Superman traveling when he hit the ground 7.8 seconds after falling? c. A water balloon was dropped from a high window and struck its target 1.1 seconds later. What was its velocity on impact? 2. Solve for Distance using D = 1 2 g t2 a. A stone tumbles into a mineshaft and strikes bottom after falling for 4.2 seconds. How deep is the mineshaft? b. A volleyball serve was in the air for 2.2 seconds before it landed untouched in the far corner of the opponent s court. What was the maximum height of the serve? c. A boy threw a small bundle toward his girlfriend on a balcony 10.0 meters above him. The bundle stopped rising in 1.5 seconds. How high did the bundle travel? Was that high enough for her to catch it? 70

Activity 9: Projectile Motion Online Lab http://galileoandeinstein.physics.virginia.edu/more_stuff/applets/projectilemotion/jarapplet.html What is the effect of Launch Angle on the motion of a projectile? Refresh the web page and set these variables: Mass = 10 kg Initial Velocity = 50 m/s Make sure the show trails is checked and that air resistance is NOT checked Angle of Launch Maximum Range (distance) Maximum Elevation (height) End Velocity Total Time (degrees) (meters) (meters) (m/s) (s) 10 20 30 40 45 50 60 70 80 90 1. At what angle was the maximum range (horizontal distance) reached? 2. At what angle was the maximum elevation achieved? 3. At what angle was the greatest "hang" time achieved? 71

4. Compare the maximum range (horizontal distance) reached for these pairs of launch angles. a. 10 o = meters and 80 o = meters b. 20 o = meters and 70 o = meters c. What pattern is observed for these angles and their maximum ranges? c. Do you notice any other paired combinations in the data table that share the same maximum range? List them: 5. A projectile is launched at an initial speed of 50 m/s with a horizontal angle of 76 o. Use the simulation to answer these questions: What is its range? State another angle that will produce the same range. a. Does the simulation verify your prediction? b. What is the sum of the two angles that produce this range?. 72

Part Two: Forces 73

Activity 10: Inertia Around A Curve What Do You Think? o Which type of car, a heavier or lighter one, needs more force to slow down with the same deceleration? Procedure: o Set up the circular track as shown to the left, and make sure it is placed where everyone in your group can easily see it. o Practice sending the metal marble counterclockwise around the inside of the circular track with enough speed to make it go around two or three times before stopping. o Set the opening to A o Predict where you think the metal marble will roll once it has gone around the circular track and travels out through the opening. o Place the miniature road cone on the table to mark the position of your prediction. o Write your observations below: 74

o o Set the opening to B Predict where you think the metal marble will roll once it has gone around the circular track and travels out through the opening. o Place the miniature road cone on the table to mark the position of your prediction. o Write your observations below: o o Set the opening to C Predict where you think the metal marble will roll once it has gone around the circular track and travels out through the opening. o Place the miniature road cone on the table to mark the position of your prediction. o Write your observations below: 75

Analysis: Change in Motion Force Responsible Marble Accelerated from Rest Marble goes in a circle Marble slows down Analysis Questions: 1) Describe the changes in direction and speed of the marbles when they traveled: a. Inside the circular track b. Outside the circular track 2) Describe the changes in the path of the marble that occurred when you changed: a. The opening position of the circular track b. The mass of the marble 76

3) Imagine that a car is approaching a curve in the road when it suddenly loses its steering and brakes. The area is flat and there is no guardrail on the road. a. On the diagram below, draw a line showing the car s path when it loses its steering and brakes. b. Explain why the car will take that path. c. How would your answer change if the car has more mass? Explain. 77

Activity 11: The Net Force Challenge What Do You Think?: o Can you describe the motion of these blocks? Procedure: Part A: Balanced Forces 1. Place the block on the table, and hook both force meters to it as shown below. Note: Each mark on the force meter is 0.1 N 2. While NOT moving the block, have one group member pull gently with 1.0 N on one force meter, while another pulls gently with 1.0 N on the other force meter. 3. Draw a force diagram of the block below. Part B: Unbalanced Forces 4. Pull gently with 1.5 N on one force meter, while another group member pulls gently with 1.0 N on the other force meter. The other group members should watch the block and observe its motion. 5. Switch roles, and repeat step 4 until each group member gets to pull the block and observe its motion. 6. Discuss with your group members the motion of the block. 7. Was the block accelerating? How do you know? 80

8. Draw another force diagram below and record the forces from step 4. Nonzero Net Force Part C: The Challenge In this part of the activity, your challenge is to decide if the forces on the block are balanced or unbalanced. 9. Unhook one of the force meters. Place two metal cylinders on the block and secure them with the rubber band as shown below. 10. Practice pulling gently on the force meter so that the block slides steadily and as slowly as possible. 11. When you can do this well, read the force needed to pull the block slowly and steadily. 12. Switch roles, and repeat steps 10 and 11 until each group member gets to pull the block and observe its motion. 13. With your group members, discuss the motion of the block. 14. Identify all the forces on the block. 15. Is the block accelerating or not? How do you know? 16. Draw a force diagram of the block at Step 11. Title your diagram Zero Net Force or Nonzero Net Force depending on the conclusion of your group. 81