Motion Unit: Part1 Speed and Acceleration Learning Targets

Transcription

1 Motion Unit: Part1 Speed and Acceleration Learning Targets These are the things that you will know and be able to do after we finish this unit: I know - the definition for speed. - the definition for velocity. - the definition for acceleration. - the units for speed. - the units for velocity. - the units for acceleration. I can - calculate the speed of an object. - calculate the velocity of an object. - calculate the acceleration of an object. - make distance vs. time graphs for an object. - make speed vs. time graphs for an object. - describe an object s motion from its distance vs. time graph. - describe an object s motion from its speed vs. time graph.

2 Name Class Date CHAPTER 11 SECTION Motion 1 Measuring Motion KEY IDEAS As you read this section, keep these questions in mind: What is motion? What is the difference between velocity and speed? How can you use graphs to show the motion of an object? What Is Motion? Objects move in many ways. Cars travel in straight lines along busy roads. Satellites travel in circles around Earth. Motion is so common that it probably seems very simple. However, in science, we must be careful to define motion precisely. Imagine sitting in a moving car with your eyes closed. If you could not see the road moving by the car, it would be hard to tell the car was moving. Motion must be defined relative to other objects. The objects used to define motion are called a frame of reference. In physics, any object can be a frame of reference. The objects that make up the frame of reference are treated as if they are not moving. In science, motion is the change in position of an object relative to a frame of reference. In the image shown below, trees provide a frame of reference for the motion of the snowboarder. READING TOOLBOX Summarize As you read, underline the main ideas in each paragraph. When you finish reading, write a summary of the section using the underlined ideas. READING CHECK 1. Define What is a frame of reference? In this multiple-exposure photograph, the trees and ski jump provide a frame of reference for the motion of the snowboarder. You can tell the snowboarder is moving because his position relative to the trees is changing. 2. Infer Give another example of a frame of reference for the motion of the snowboarder. When we describe motion, we are often interested in how far an object has moved. Scientists describe how far an object has moved using two terms: distance and displacement. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 229 Motion

3 Name Class Date SECTION 1 Measuring Motion continued DISTANCE AND DISPLACEMENT You are probably familiar with what distance means. Distance is how far an object moves. If you run one lap around a soccer field, you have run a distance of about 350 m. In contrast, displacement is a measure of how far the starting point is from the ending point. If you run seven laps around a soccer field and end up exactly where you started, your displacement is 0 m. In many cases, displacement is shorter than distance. Distance traveled 3. Identify Which is longer, the runner s distance traveled or displacement? Displacement When you describe distance and displacement, you need to give both a length and a direction. You can describe the direction of displacement using cardinal directions, such as north, south, east, or west. You can also describe direction relative to a reference point. For example, in the figure above, the direction of the student s displacement could be described as away from the goal. 4. Apply Concepts A scientist records the motion of an object in a notebook. She writes down that the object moved 10 m in 3 s. Did the scientist record a speed or a velocity? Explain your answer. How Are Speed and Velocity Different? In everyday language, we often use the words speed and velocity as if they mean the same thing. However, in science, speed is different from velocity. You know from experience that some objects travel faster than others. A running horse travels faster than a jogger. A race car travels faster than a running horse. Speed describes how far an object travels in a certain amount of time. In other words, it describes how fast an object moves. In contrast, velocity describes both how fast an object is moving and in what direction it is moving. As when you describe displacement, you can describe the direction of motion using words such as up, down, left, and right. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 230 Motion

4 Name Class Date SECTION 1 Measuring Motion continued Wheelchair racer 7.3 m/s Distance vs. Time Speeding race car Galloping horse 19 m/s Speeding race car 96 m/s Distance (m) Galloping horse Wheelchair racer Time (s) 5. Apply Concepts Could you determine the velocities of these objects from the information in the graph? Explain your answer. Objects can move at many different speeds. The faster the object is moving, the steeper the slope of its line on a graph of distance versus time. ADDING VELOCITIES Imagine a person sitting on a bus. The bus is traveling east at 15 m/s relative to the street. The person gets up and walks toward the back of the bus at 1 m/s. How can you determine the person s velocity relative to the street? Before the person starts walking, her velocity is the same as the bus 15 m/s east relative to the street. However, when she is walking toward the back of the bus, her velocity decreases. You can use positive and negative numbers to figure out the person s velocity when she is walking on the bus. First, you have to define which direction is positive motion. In this case, you can define positive motion as motion eastward. Therefore, the bus and everyone on it has a velocity of 15 m/s. The person walking toward the back of the bus is moving in the opposite direction from the bus. Therefore, she has a negative velocity. Her velocity is 1 m/s. To determine her total velocity, add the two velocities together. Her total velocity is ( 15 m/s) ( 1 m/s) = 14 m/s. Since we have defined positive motion as motion eastward, the person is moving 14 m/s east. 6. Predict Consequences Suppose you defined positive motion as motion westward. What would be the person s total velocity? Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 231 Motion

5 Name Class Date SECTION 1 Measuring Motion continued READING CHECK 7. Identify What two quantities do you need to know to calculate speed? How Can You Calculate Speed? Remember that speed describes the distance an object travels in a certain amount of time. Therefore, to calculate speed, you need to measure two quantities: the distance traveled and the time it took. The SI unit for speed is m/s. Some objects move at a constant speed. Others move at variable speeds. A horse that runs a distance of 19 m every second is running at a constant speed of 19 m/s. If the horse stops, its speed changes from 19 m/s to 0 m/s. In that case, the horse has a variable speed. 8. Infer It is often easier to calculate the average speed of an object than to calculate its speed at each point along its path. What do you think is the reason for this? AVERAGE SPEED Most objects do not travel at one constant speed. Instead, their speed changes from one instant to another. In this case, it is often useful to describe the average speed of the object. Average speed is the total distance traveled divided by the total time it took to travel that distance. The equation below describes this relationship: speed = distance time v = d t Let s look at an example. A sledder moves 132 m down a hill in 18 s. What is the average speed of the sledder? Step 1: List the given and unknown values. Given: distance, d = 132 m Unknown: average speed, v time, t =18 s Step 2: Write the equation. Step 3: Insert the known values and solve for the unknown value. v = d t v = 132 m 18 s v = 7.3 m/s So, the sledder has an average speed of 7.3 m/s. The sledder s speed may have changed many times as he moved down the hill. At some points, he may have been traveling faster than 7.3 m/s. At other points, he may have been moving more slowly. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 232 Motion

6 Name Class Date SECTION 1 Measuring Motion continued INSTANTANEOUS SPEED The instantaneous speed of an object is its speed at a given instant, or point in time. Because we cannot divide by zero, we cannot use the equation for speed to calculate instantaneous speed. However, tools like the speedometers in cars can measure instantaneous speed. If an object is moving at a constant speed, its instantaneous speed is equal to its constant speed. How Can You Calculate Velocity? Remember that velocity is the speed of an object in a particular direction. To calculate the velocity of an object, you must first find the speed of the object. Then, you must indicate the direction of the object. Let s look at an example. For several days in 1936, Alaska s Black Rapids glacier moved at 89 m per day down the valley. What is the velocity of the glacier in meters per second? READING CHECK 9. Explain Why can t you use the speed equation to calculate instantaneous speed? Step 1: List the given and unknown values. Step 2: Perform conversions, and write the equation. Step 3: Insert the known values and solve for the unknown value. Given: d = 89 m t = 1 day direction = down the valley 1 day 24 h 1 day v = d t 60 min 1 h Unknown: velocity, v v = 89 m 86,400 s v = m/s down the valley 60 s 1 min = 86,400 s Math Skills 10. Calculate A swimmer swims 110 m toward the shore in 72 s. What is the swimmer s velocity in meters per second? Show your work. So, the glacier moved at a velocity of m/s down the valley. Notice that the symbol for velocity, v, is the same as the symbol for speed. You can use the speed equation to calculate velocity. Just remember to include a direction when you describe an object s velocity. How Can You Show Motion on a Graph? You can show motion on a graph by recording distance on the vertical axis and time on the horizontal axis. Then, you can use the shape of the line on the graph to learn about the motion of an object. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 233 Motion

7 Name Class Date SECTION 1 Measuring Motion continued READING CHECK 11. Describe On a graph of distance versus time, what does the motion of an object moving at a constant speed look like? CALCULATING SPEED FROM A GRAPH On a graph of distance versus time, the motion of an object moving at a constant speed is a straight line. The slope of the line is equal to the speed of the object. You can calculate the slope of the line by dividing the vertical change of the line by its horizontal change. The equation below describes this relationship: vertical change slope = horizontal change If you show distance on the vertical axis and time on the horizontal axis, the slope of the line is: change in distance slope = change in time Remember that speed equals distance divided by time. Therefore, the slope of a line on a graph of distance versus time is the speed of the object. For example, you can determine the speed of the object in the plot below. Graphing Skills 12. Identify What is the independent variable in the graph in the figure? 13. Apply Concepts Suppose you chose two different points on the line to calculate slope. Would you get the same result for slope? Explain your answer. Distance (m) Step 1: Choose two points to use to calculate the slope. Step 2: Calculate the vertical change and the horizontal change Distance vs. Time horizontal change = 3 s vertical change = 6 m Time (s) Point 1: time, t = 1 s distance, d = 6 m Point 2: time, t = 4 s distance, d = 12 m vertical change = 12 m 6 m = 6 m horizontal change = 4 s 1 s = 3 s Step 3: Divide the vertical change by the horizontal change. vertical change slope = horizontal change = 6 m 3 s = 2 m/s So, the slope of the line and the speed of the object is 2 m/s. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 234 Motion

8 Name Class Date SECTION 1 Measuring Motion continued INTERPRETING SLOPE Remember that the speed of an object is equal to the slope of the line describing its motion. The steeper the slope of the line, the faster the object is moving. For example, the graphs below show the motion of two cars traveling at different constant speeds. Distance (m) Fast-Moving Car Time (s) Distance (m) Slow-Moving Car Time (s) The slopes of the lines on these graphs indicate the speeds of the cars. The graph of the motion of a fast-moving car has a steeper slope than that of a slow-moving car. The fact that these graphs are straight lines indicates that the cars are moving at constant speeds. 14. Identify How can you tell that the cars are moving at constant speeds based on the information in the graphs? On a graph of distance versus time, the motion of an object moving at a variable speed is a curved line. For example, the graph below shows distance versus time for a car that is speeding up. Distance (m) Car with Changing Speed Time (s) The graph of this car s motion is not a straight line. Therefore, the car is not moving at a constant speed. Graphing Skills 15. Apply Concepts What is the car s average speed between 0 s and 5 s? Show your work. Even if an object s speed is changing, you can use a graph of its motion to find its average speed. Remember that average speed equals total distance traveled divided by total time. You can find both total distance and total time from the graph. Then, divide distance by time to calculate average speed. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 235 Motion

9 Name Class Date Section 1 Review SECTION VOCABULARY displacement the change in position of an object frame of reference a system for specifying the precise location of objects in space and time motion an object s change in position relative to a reference point speed the distance traveled divided by the time interval during which the motion occurred velocity the speed of an object in a particular direction 1. Describe How is a frame of reference used to describe motion? 2. Interpret Label the fastest moving object and the slowest moving object in the plot below. Explain your reasoning for selecting each line Distance vs. Time Distance (m) Time (s) 3. Apply Concepts A runner runs a 1,500 m race on a circular track. The runner stops 100 m from the starting point. What are the distance and displacement traveled by the runner? 4. Calculate Scientists tracking a flock of ducks found that, on average, the ducks flew 740 km south in 12 h. What were the speed and velocity of the flock of ducks in meters per second? Show your work. Copyright by Holt, Rinehart and Winston. All rights reserved. Interactive Reader 236 Motion

10 Running in the Halls! Today we are going to take over the halls of CPHS! We are going to measure the speed of three different students, graph the results and learn how much a graph can really tell us! Getting Started: Volunteers needed: 1 walker, 1 speed walker and 1 runner Student timers (you get to use a stopwatch!) Walker Speed Walker Runner Walk very slowly at a Walk at a constant speedy Run at a constant rate constant rate rate Part One: Let s Make Some Predictions! In today s lab, we are going to analyze the motion of a walker, a speed walker and a runner. We will end up making distance time graphs for each person. A distance time graph shows the distance an object (or person) moves over a given amount of time. Before we begin the lab, predict what the distance time graph for each student will look like: Walker Speed Walker Runner d d d t t t

11 Part Two: Collecting the Data Record the times for the walker, the speed walker and the runner on the table below: Time (seconds) Distance (meters) Walker Speed Walker Runner

12 Part Three: Graphing the Data On the graph below, make a distance-time for the walker, the speed walker and the runner (one graph with three lines on it). You should use a different color for each person. Please draw the best fit line for each person s data. NOTE: Look at your Graph Requirements sheet (in your 3-ring binder) to see which axis should be Time and which should be Distance.

13 Part Four: Calculations and Questions Use your data and your graph to answer the following questions: 1. Calculate the average speed for each of the students. Show your work. (Speed = Distance Time) Walker Speed Walker Runner 2. Describe the slope of each line. (The slope refers to the steepness of the line. A steeper line has a greater slope.) Walker Speed Walker Runner 3. The steeper the line, the the person is moving. 4. The steepness of the line (the slope of the line) tells you about the speed of the person, what does the fact that the line is a straight line tell you about the person s motion? Prediction Time! The Runner was running at a constant speed. Predict what you think the graph of his/her Speed versus Time will look like: Runner s t Why do you think the graph will look this way?

14 Part Five: Calculating Speed Look at your line that you drew for the Runner. Pick any 5 points on the line and record their distances and times on the table below. Use those numbers to calculate the speed of the Runner at each of those points. Round your speeds to the nearest tenth! Point Distance Time = Speed Part Six: Graphing Speed Make a speed-time graph of your data from Part Five. Draw the best-fit line for your data. NOTE: Look at your Graph Requirements sheet (in your 3-ring binder) to see which axis should be Time and which should be Speed.

15 Part Seven: Questions Use your speed-time data and graph to answer the following questions. 1. Describe what your best-fit line looked like? 2. Why does the line look this way? 3. How would this graph change if the runner had increased his/her speed during the race? 4. How would this graph change if the runner had slowed down during the race? 5. What would you expect the speed-time graphs for the walker and the speed walker to look like? Part Eight: Wrap-Up Here, in a nice summary format, are the main points of today s lab: 1. A distance-time graph is a way to show the movement of an object. 2. The slope (steepness) of a line on a distance-time graph is related to the speed of the object. A steep line equals greater speed and a less steep line equals lower speed. 3. On a distance-time graph, a straight line means that the speed was constant (it wasn t changing). 4. The formula for calculating speed is Speed = Distance Time. 5. A speed-time graph shows how an object s speed changes over time. 6. On a speed-time graph, a flat line means that the speed was constant (it wasn t changing)

16 Speed Calculations Name: Part 1: The Units for Speed What do the following units represent? Use D for distance, T for time, or S for speed km 3. 6 hours mi 7. 3 km/hr m/s cm/s sec 8. 6 mm/se Part 2: Speed, Distance and Time Calculations Complete the following formulas before you solve the problems below. Formula #1 Speed = Distance Time Formula #2 Distance = Formula #3 Time = Solve the following problems. Show all of your work! 1. A football field is about 100 m long. If it takes a person 20 seconds to run its length, how fast (what speed) were they running? 2. The pitcher s mound in baseball is 85 m from the plate. It takes 4 seconds for a pitch to reach the plate. How fast is the pitch? 3. If you drive at 100 km/hr for 6 hours, how far will you go? 4. If you run at 12 m/s for 15 minutes, how far will you go? 5. A bullet travels at 850 m/s. How long will it take a bullet to go 1 km? 6. The fastest train in the world moves at 500 km/hr. How far will it go in 3 hours?

17 7. How long will it take light moving at 300,000 km/s to reach us from the sun? The sun is 150,000,000 km from earth. Convert your answer to minutes. Part 3: Interpreting a Distance-Time Graph The graph below describes the motion of a person. Distance D I S T A N C E (m) E D C B F A Distance Time (seconds) 1. At what point(s) was the person moving away from the starting point? 2. At what point(s) was the person standing still? 3. At what point(s) was the person moving towards the starting point? 4. At what point(s) was the person moving away the fastest? 5. At what point(s) was the person moving with a constant speed? 6. At what time(s) was the person 15 meters away from the starting point? 7. At what point(s) was the person 45 meters away from the starting point? 8. Use the information on the graph to calculate the average speed of the person.

18 Bowling for Knowledge Accelerated Learning You know how to calculate speed. You know what a Distance vs. Time graph can tell you about an object s motion. You have even been moved by my bad jokes. So far, you own the Motion Unit. Well, today we are going to ramp things up a bit. You are going to learn about acceleration by bowling. Specifically, we are going to roll a bowling ball down a ramp and measure how its speed changes. So let s strike out, give it our best shot and I will spare you any more terrible bowling puns! Background Information First of all, you need a definition of acceleration. Acceleration is a change in an object s velocity. The only problem with that is we don t have a definition for velocity yet. Velocity is an object s speed and direction. Sixty miles per hour is a speed. Sixty miles per hour - north is a velocity. If any part of an object s velocity changes, then the object has accelerated. Today, we are going to change an object s speed (which is part of its velocity) and analyze its acceleration. Procedure We are going to set up an 18 meter long course on the lower level Field House ramp. We will start at the top of the ramp and mark off every 2 meters. One person will release the bowling ball, while timers at each of the 2-meter marks will record the time when the bowling ball goes past them. At the bottom of the ramp, someone will stop the ball and bring it back up to the top of the ramp. We will do 5 trials and then head back to the classroom to do the data analysis. NOTE: If the bowling ball hits the wall or the railing before it reaches the bottom of the ramp, we won t count that trial and we will do it over.

19 Data: Record your data on the following table. Distance (meters) Time (seconds) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Average Split Time* Instantaneous Speed (m/s)** 2m split time *: The split time is the time that it took for the bowling ball to go from one checkpoint to the next. To find the split time you just take the time for the checkpoint that you are at and subtract the previous checkpoint s time from it. For example, if the time for the 8m mark is 6.5 seconds and the time for the 6m mark is 5 seconds, the split time for the 8m mark would be 6.5 seconds 5 seconds = 1.5 seconds. That means that it took 1.5 seconds for the bowling ball to go from 6m to 8m. **: The instantaneous speed is the speed an object is travelling at a particular instant. We are trying to find out the bowling ball s acceleration and we can t do that unless we know the speed of the bowling ball at each of the checkpoints. Look at it this way: Let s pretend that it took the bowling ball 9 seconds to reach the 18m point of the course. Since speed = distance time, the average speed would have been 18m 9 seconds = 2m/s. Was the bowling ball travelling this fast all of the time? Of course not! At the beginning of the course, it wasn t moving at all. Its speed was 0 m/s. So, just like the speed at the beginning was below the average speed (0m/s compared to 2m/s), the speed at the end of the course is above the average speed (In this example it would be 4m/s, twice the average speed! If you don t believe me, check out the math and see what you get). Basically, with the instantaneous speed, we are just breaking down the course into smaller, 2m segments. We can calculate the average speed of the bowling ball over each of these segments.

20 Graph #1: Distance vs. Time Make a graph of the distance the bowling ball travelled versus the average time that it took to get there. Make sure to label everything correctly! 1. Draw the line or curve that best fits the data that you just graphed. Which one did you choose? Why? 2. What made the bowling ball go down the ramp? 3. Why did the speed go down at during the middle of the course? (Hint: What was different about the ramp?)

21 Graph #2: Speed vs. Time Make a graph of the instantaneous speed of the bowling ball versus the average time. Make sure to label everything correctly! 1. Draw in the best fit line or curve for the data. Which one did you choose? Why? 2. Was the bowling ball accelerating? How does the graph show this? 3. Was the acceleration constant? (Did the speed change by the same amount each interval?)

22 Analysis/Review Questions: 1. In any graph, a straight line means that something (speed, acceleration, etc.) is. 2. What would each of these lines mean on the different graph types? Line On a Distance vs. Time Graph it means. On a Velocity vs. Time Graph it means. 3. If you only had a distance vs. time graph to look at, how could you tell if an object was accelerating? (Hint: Remember the definitions for acceleration and velocity!) 4. In the box below, draw the velocity vs. time graph for an object that moved away from the starting point and ended up right back there.

23 Here is what we have learned from doing the Running In the Halls and Bowling for Knowledge labs: 1. Speed = Distance Time 2. Velocity is an object s speed and direction. 3. Acceleration is a change in an object s velocity. 4. If an object changes its speed and/or direction, it is accelerating. 5. A straight line on a distance vs. time graph means constant speed. 6. A straight line on a speed vs. time graph means constant acceleration. 7. The steeper the slope, the greater the speed or acceleration.

24 Acceleration Acceleration is defined as a change in speed or direction. In other words it is a change in an object s velocity. Acceleration can be either positive or negative. For example, when a car slows down, its speed is changing, therefore it is accelerating. If you calculate the car s acceleration, you will get a negative number for the answer sometimes we call this decelerating. Use the formulas below to work through the following problems. FORMULAS Acceleration = Final velocity Initial velocity Time Time = Final Velocity Initial Velocity Acceleration Acceleration due to gravity = 9.8 m/s 2 Problems 1. A Porsche 911 can go from 0 to 60 mph in 3.4 seconds. What is its acceleration? (your answer will be in miles/hour/second)

25 2. If you are riding your bike and hit a curb, you would stop suddenly. Let s say that you were going 25 m/s when you hit the curb and it took you only.75 seconds to stop after hitting the curb. What was your acceleration? 3. If you were in a car going 275 m/s and a deer runs out in front of you. You slammed on the brakes to avoid hitting the deer. It took 2.5 seconds to slow to 83 m/s. What was your acceleration? 4. Gravity causes you to accelerate at 9.8 m/s/s. If a rock falls from a cliff, how fast would it be going after 4 seconds? 5. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration?

26 6. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard s average acceleration? 7. Josh rolled a bowling ball down a lane in 2.5 s. The ball traveled at a constant acceleration of 1.8 m/s/s down the lane and was traveling at a speed of 7.6 m/s by the time it reached the pins at the end of the lane. How fast was the ball going when it left Josh s hand? 8. A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at -4.0 m/s 2?

27 THE CAR RACE Name The graph below represents three cars during the first minute of a race. Using the following information, draw another curve on the grid representing the motion of Car D. This car moves as follow: 1. Car D accelerates from rest position at 0 seconds to reach a speed of 208 m/s at 5 seconds. 2. Car D maintains this speed for 5 seconds, and then accelerates to 32 m/s at 20 seconds. 3. It then accelerates to reach a speed of 160 m/s at 30 seconds and maintains this speed for 5 seconds. 4. Car D then accelerates to 112 m/s at 40 seconds, slows down further to 64 m/s at 50 seconds, and then accelerates to 208 m/s at 55 seconds The Car Race Car A Car B Car C Car D Speed (m/s) Time (s) 1. What does the vertical axis represent? 2. What does the horizontal axis represent? 3. Over which time period is Car A s acceleration the greatest? 4. At what time is Car A s speed the greatest? 5. Over which time period is Car B s acceleration the greatest? S09MW m/s throughout.

28 6. At what time is Car B s speed the greatest? 7. Over which time period is Car C s acceleration the greatest? 8. At what time is Car C s speed the greatest? 9. Over which time period is Car D s acceleration the greatest? 10. At what time is Car D s speed the greatest? 11. What is car B s speed at 10 seconds? 12. Over which time period is Car A s acceleration at zero? 13. Over which time period is Car B s acceleration at zero? 14. Over which time period is Car C s acceleration at zero? 15. Which car has traveled the farthest at the end of one minute? Explain how you know: 16. Which car has appears to have a reckless driver? Explain how you know: 17. Which car s engine appears to have stalled during the race? Explain how you know: 18. What is the acceleration of Car A from 0 to 60 seconds? Is this constant acceleration? How do you know? 19. What is the acceleration of Car B from 0 to 10 seconds? 20. What is the acceleration of Car B from 15 to 60 seconds? 21. Describe Car C s motion during the 60 seconds. 22. What is the acceleration of Car C from 5 to 60 seconds? 23. What is the acceleration of Car D from 0 to 60 seconds? 24. Does this average acceleration give an accurate depiction of how fast car D traveled? Explain. S09MW m/s throughout.

29 Graphing Your Motion Today is all about you. You are going to graph your own motion, you are going to move around in an attempt to match already graphed motion, you are going to use some really cool equipment and you are going to buy your teacher a present (well, 3 out of 4 isn t bad!). Have a great time, be careful with the equipment, help each other out and enjoy a truly moving lesson! Today s Goals: When you are done with today s lab, you should be able to 1. Look at a distance (position) vs. time graph and describe the motion it shows. 2. Look at a velocity vs. time graph and describe the motion it shows. 3. State the definitions for speed, velocity and acceleration. 4. Explain the relationship between the slope of a line and an object s speed. 5. Explain the relationship between the slope of a line and an object s acceleration. Materials - Logger Pro - Motion Detector - A book, or some other flat surface, to hold in front of you as you move towards and away from, the motion detector. Procedure: 1. Connect the motion sensor to the Lab Quest. The cable goes in the DIG slots. 2. Plug the Lab Quest in (use the power supply). 3. Turn on your Lab Quest (it will take a while to turn on). 4. Select Sensors and then select Data Collection. 5. Change the length from 5 seconds to 10 seconds and the interval to 0.5 seconds. Select Okay. 6. Touch the icon that looks like a graph. 7. Select Graph and then select Show Graph. Select Graph When you are using the motion detector, make sure to hold a flat surface in front of you. 9. Open the sensor up (the sensor pops up so that it is perpendicular to the ground). 10. To start collecting data, push the button. Part A: Distance (Position) vs. Time Graphs Background: In the first part of this lab, we are going to look at distance that you travel in a given amount of time. You are going to move away and towards a motion sensor. A graph will be made that shows where you were in relationship to the sensor at any given time. When you make a distance (or position) vs. time graph, the line that you get tells you about your speed. The formula for speed is: Speed = Distance Time. On your graphs the slope of the line equals

30 your speed. In the case of your graphs, if you go away from the detector, you should get a line with a positive slope (it looks like this / ) and if you walk towards the detector, you should get a line with a negative slope (it looks like this \ ). 1. Discuss each situation described below and sketch a prediction for the graph of the indicated motion. Once you have made a prediction, actually do the motion and draw what the graph looks like. MOTION: Move away from the detector at a constant speed. Predicted Actual Distance Time Time MOTION: Move towards the detector at a constant speed. Predicted Actual Distance Distance Distance Time Time MOTION: Walk away from the detector at a constant speed, then stop, and then walk towards the detector at a constant speed. Predicted Actual Distance Distance Time Time

31 MOTION: Start walking slowly away from the detector and continuously speed up. Then stop and remain still. Predicted Actual Part B: It s Your Time to Shine! In this section, each person in the group is going to match two motion graphs each. No two of these graphs will be the same. On the grids below, sketch what graphs the computer gave you to match and draw your best attempt on top of it. Here s how you get the graphs for you to match: 1. Choose Analyze 2. Choose Motion Match. 3. Choose New Position Match. 1 st Match 2 nd Match Distance Distance Distance Distance Time Time Time Time

32 Part C: Distance vs. Time Questions 1. What did your graphs look like when you travelled at a constant speed? Were the lines straight or curved? 2. When were the lines steepest when you were travelling fast or slow? 3. What was going on when the lines were flat? Part D: Velocity vs. Time Graphs **Please notice that these graphs will look very different because these graphs show velocity on the x-axis instead of time. NOTE: Velocity is your speed and your direction. A negative velocity means that you are moving towards the detector and a positive one means that you are moving away. 1. Again, predict what you think the graph will look like before using the computer. 2. Select Sensors and then select Data Collection. 3. Change the length from 5 seconds to 10 seconds and the interval to 0.5 seconds. Select Okay. 4. Touch the icon that looks like a graph. 5. Select Graph and then select Show Graph. Select Graph When you are using the motion detector, make sure to hold a flat surface in front of you. 7. Open the sensor up (the sensor pops up so that it is perpendicular to the ground). 8. To start collecting data, push the button. Background: In the second part of this lab, we are going to look at the velocity that you travelled at in a given amount of time. You are going to move away and towards a motion sensor. A graph will be made that shows velocity towards, and away from, the sensor at any given time. When you make

33 a velocity vs. time graph, the line that you get tells you about your acceleration. Velocity is just your speed and your direction. Acceleration describes a change in your velocity. On your graphs the slope of the line equals your acceleration. If you walk away from the detector, your graph should be above zero and if you walk towards it, your graph should be below zero. MOTION: Move away from the detector at a constant speed. Predicted Actual Velocity Velocity Time Time MOTION: Move towards the detector at a constant speed. Predicted Actual Velocity Velocity Time Time

34 MOTION: Walk away from the detector at a constant speed, then stop and then walk towards the detector at a constant speed. Predicted Actual Velocity Velocity Time Time MOTION: Start walking slowly away from the detector and continuously speed up. Then stop and remain still. Predicted Actual Velocity Velocity Time Time

35 Part E: It s Your Time to Shine (again)! In this section, each person in the group is going to match two velocity graphs each. No two of these graphs will be the same. On the grids below, sketch what graphs the computer gave you to match and draw your best attempt on top of it. Here s how you get the graphs for you to match: 1. Choose Analyze 2. Choose Motion Match. 3. Choose New Velocity Match. 1 st Match 2 nd Match Velocity Velocity Time Time Part F: Velocity vs. Time Questions 1. What did your graphs look like when you travelled at a constant velocity? Were the lines straight or curved? 2. When were the lines steepest when you were accelerating quickly or slowly? 3. What was going on when the lines were flat?

36 Part G: Analysis Questions 1. If this graph is a distance vs. time graph a. How would you have to walk to match part A on the graph? b. How would you have to walk to match part B on the graph? Distance (m) A B Time 2. If this graph is a velocity vs. time graph a. How would you have to walk to match part A on the graph? b. How would you have to walk to match part B on the graph? Velocity (m/s) e A Time B

37 Motion Graphs 1 Name Motion Graphs Describing the motion of an object is occasionally hard to do with words. Sometimes graphs help make motion easier to picture, and therefore understand. Remember: Motion is a change in position measured by distance and time. Speed tells us the rate at which an object moves. Velocity tells the speed and direction of a moving object. Acceleration tells us the rate speed or direction changes. DISTANCE-TIME GRAPHS Plotting distance against time can tell you a lot about motion. Let's look at the axes: Time is always plotted on the X-axis (bottom of the graph). The further to the right on the axis, the longer the time from the start. Distance is plotted on the Y-axis (side of the graph). The higher up the graph, the further from the start. If an object is not moving, a horizontal line is shown on a distance-time graph. Time is increasing to the right, but its distance does not change. It is not moving. We say it is At Rest. M. Poarch

38 Motion Graphs 2 If an object is moving at a constant speed, it means it has the same increase in distance in a given time: Time is increasing to the right, and distance is increasing constantly with time. The object moves at a constant speed. Constant speed is shown by straight lines on a graph. Let s look at two moving objects: Both of the lines in the graph show that each object moved the same distance, but the steeper dashed line got there before the other one: A steeper line indicates a larger distance moved in a given time. In other words, higher speed. Both lines are straight, so both speeds are constant. Graphs that show acceleration look different from those that show constant speed. The line on this graph is curving upwards. This shows an increase in speed, since the line is getting steeper: In other words, in a given time, the distance the object moves is change (getting larger). It is accelerating. M. Poarch

39 Motion Graphs 3 Summary: A distance-time graph tells us how far an object has moved with time. The steeper the graph, the faster the motion. A horizontal line means the object is not changing its position - it is not moving, it is at rest. A downward sloping line means the object is returning to the start. (Graph from: M. Poarch

40 Motion Graphs 4 Examine the graphs below. of runners started 10 yards further ahead of the other? Whic h of the follo wing graph s indica tes that one Which of the graphs shows that one of runners started 10 yards further ahead of the other? Explain your answer. In M. Poarch

41 Motion Graphs 5 In which of the following graphs below are both runners moving at the same speed? Explain your answer. M. Poarch

42 Motion Graphs 6 The distance-time graphs below represent the motion of a car. Match the descriptions with the graphs. Explain your answers. Descriptions: 1. The car is stopped. 2. The car is traveling at a constant speed. 3. The speed of the car is decreasing. 4. The car is coming back. Graph A matches description because. Graph B matches description because. Graph C matches description because. Graph D matches description because. M. Poarch

43 Motion Graphs 7 SPEED-TIME GRAPHS Speed-Time graphs are also called Velocity-Time graphs. Speed-Time graphs look much like Distance- Time graphs. Be sure to read the labels!! Time is plotted on the X-axis. Speed or velocity is plotted on the Y-axis. A straight horizontal line on a speed-time graph means that speed is constant. It is not changing over time. A straight line does not mean that the object is not moving! This graph shows increasing speed. The moving object is accelerating. This graph shows decreasing speed. The moving object is decelerating. M. Poarch

44 Motion Graphs 8 What about comparing two moving objects at the same time? Both the dashed and solid line show increasing speed. Both lines reach the same top speed, but the solid one takes longer. The dashed line shows a greater acceleration. Summary: A speed - time graph shows us how the speed of a moving object changes with time. The steeper the graph, the greater the acceleration. A horizontal line means the object is moving at a constant speed. A downward sloping line means the object is slowing down. (Graph from: M. Poarch

45 Motion Graphs 9 The speed-time graphs below represent the motion of a car. Match the descriptions with the graphs. Explain your answers. Descriptions: 5. The car is stopped. 6. The car is traveling at a constant speed. 7. The car is accelerating. 8. The car is slowing down. Graph E matches description because. Graph F matches description because. Graph G matches description because. Graph H matches description because. M. Poarch

46 Motion Graphs 10 Questions: ( Some questions adapted from Look at the graph above. It shows how three runners ran a 100-meter race. Which runner won the race? Explain your answer. Which runner stopped for a rest? Explain your answer. How long was the stop? Explain your answer. How long did Bob take to complete the race? Explain your answer. Calculate Albert s average speed. (Figure the distance and the time first!) M. Poarch

47 Motion Graphs 11 The graph below shows how the speed of a bus changes during part of a journey Choose the correct words from the following list to describe the motion during each segment of the journey to fill in the blanks. accelerating decelerating constant speed at rest Segment 0-A The bus is. Its speed changes from 0 to 10 m/s in 5 seconds. Segment A-B The bus is moving at a of 10 m/s for 5 seconds. Segment B-C The bus is. It is slowing down from 10 m/s to rest in 3 seconds. Segment C-D The bus is. It has stopped. Segment D-E The bus is. It is gradually increasing in speed. M. Poarch