Lesson 3 Acceleration Student Labs and Activities Page Launch Lab 45 Content Vocabulary 46 Lesson Outline 47 MiniLab 49 Content Practice A 50 Content Practice B 51 Language Arts Support 52 Math Skills 54 School to Home 55 Key Concept Builders 56 Enrichment 60 Challenge 61 Lab A 64 Lab B 67 Lab C 70 Chapter Key Concepts Builder 71 44 Describing Motion
Launch Lab LESSON 3: 10 minutes In what ways can velocity change? As you walk, your motion changes in many ways. You probably slow down when the ground is uneven. You might speed up when you realize that you are late for dinner. You change direction many times. What would these changes in velocity look like on a distance-time graph? 6 Distance (m) 3 0 5 10 15 Time (s) 20 25 30 Procedure 1. Read and complete a lab safety form. 2. Use a meterstick to measure a 6-m straight path along the floor. Place a mark with masking tape at 0 m, 3 m, and 6 m. 3. Look at the graph above. Decide what type of motion occurs during each 5-second period. Think About This 4. Try to walk along your path according to the motion shown on the graph. Have your partner time your walk with a stopwatch. Switch roles and repeat this step. 1. What does a horizontal line segment on a distance-time graph indicate? 2. Key Concept According to the graph, at what times do the following motions take place? a. You change direction. b. Your speed increases. c. Your speed decreases. Describing Motion 45
Content Vocabulary LESSON 3 Acceleration Directions: In this word search puzzle, find and circle the four terms listed below. Then on each line, write the term that correctly completes each sentence. acceleration horizontal vertical A T E C Q K K E L Z P S N H A F C Z A S V K Y Q Y R P P P H A O P B U B F C J L E J U Y L M N R O R G U G X M W C P K L R S V G K N W I C E L J S Z I E Y V J I A E D U P Z E F T K Y L M D L J Q V T F G B E O G K M X I V V J R E N J T K C F E N M R H B E B V M Y W R H D R Z R C T A Y Y K E E D O B X D A F G X Q R A P P C O E P P U D H C X T Q N N C L E P O H C X M S Q S A M O I N Z J L N O Y Z D E E G C D G Q C Y O V M G A T Y F C X Q Y L V X I D K A N V R P D Q U W R E B V W E P Y U G Q M E O U M Z S Z E K C C F J R G P B Y K L A C I T R E V M L X Y Z X A S U O Z N T N W Z V F C N M R S E L I T Q Z L T L S T D O F D P Q Q Z V W I X I I U T X D W B E V G T T L T D Y U Z C O Q M K N P O S F D J E H L B Y V L H L N 1. The axis, or x-axis, of a graph runs from left to right across a page. 2. The axis, or y-axis, of a graph runs upright on a page. 3. is a measure of the change in velocity during a period of time. 46 Describing Motion
Lesson Outline LESSON 3 Acceleration A. Acceleration Changes in Velocity 1. is a measure of the change in velocity during a period of time. 2. An object accelerates when its velocity changes as a result of increasing speed, decreasing speed, or a change of. 3. Like velocity, acceleration has a direction and can be represented by a(n). 4. An acceleration arrow s direction depends on whether the increases or decreases. a. When the velocity of an object is increasing, the acceleration arrow points in the direction as the velocity arrows. b. When the velocity of an object is decreasing, the acceleration arrow points in the direction as the velocity arrows. 5. When an object changes direction, the acceleration arrows point to the B. Calculating Acceleration of the curve along which the object is moving. 1. is a change in velocity during a time interval divided by the time interval during which the velocity changes. 2. If SI units are used in the acceleration equation, then acceleration has units of. 3. If acceleration is negative, then it is the direction of motion. C. Speed-Time Graphs 1. A(n) can be used to show how speed changes over time. 2. A speed-time graph has plotted on the horizontal axis, which is the x-axis. which is the y-axis. is plotted on the vertical axis, 3. The speed-time graph for an object at is a horizontal line at y = 0. Describing Motion 47
Lesson Outline continued 4. If an object is moving at speed, its speed-time graph is a horizontal line above the x-axis. 5. The speed-time graph for an object that is speeding up is a line that slants toward the right side of the graph. 6. If an object is slowing down, its speed-time graph is a line that slants toward the right side of the graph. 7. Speed-time graphs do not show what happens when velocity changes as the result of a change of. D. Summarizing Motion 1. can be described by one s direction and distance from a reference point. 2. Distance and displacement can be compared to find one s average. 3. Speed and direction describe one s. 4. If one s velocity is, that person is accelerating. 48 Describing Motion
MiniLab LESSON 3: 10 minutes How is a change in speed related to acceleration? What happens if the distance you walk each second increases? Follow these steps to demonstrate acceleration. Procedure 1. Read and complete a lab safety form. 2. Use masking tape to mark a course on the floor. Mark start, and place marks along a straight path at 10 cm, 40 cm, 90 cm, 160 cm, and 250 cm from the start. 3. Clap a steady beat. On the first beat, the person walking the course is at start. On the second beat, the walker should be at the 10-cm mark, and so on. Data and Observations Analyze and Conclude 1. Explain what happened to your speed as you moved along the course. 2. Key Concept Suppose your speed at the final mark was 0.95 m/s. Calculate your average acceleration from start through the final segment of the course. Describing Motion 49
Content Practice A LESSON 3 Acceleration Directions: On each line, write the term from the word bank that correctly completes each sentence. Each term is used only once. backward constant decreasing direction forward increasing speed velocity x-axis y-axis 1. A moving object undergoes an acceleration when its or changes. 2. When a moving object slows down, its acceleration and are in opposition. 3. When a moving object slows down, an arrow representing its acceleration flips from to. 4. On a speed-time graph, speed is plotted on the, and time is on the. 5. On a speed-time graph, a(n) speed is shown by a line going upward from the left. 6. On a speed-time graph, a(n) speed is shown by a line going downward to the right. 7. On a speed-time graph, a(n) speed is represented by a horizontal line. 50 Describing Motion
Content Practice B LESSON 3 Acceleration Directions: On the speed-time graph below, draw a line showing the motion of a test car that moved forward at a speed of 50 km/h and crashed into a barrier at the 5-second mark. Continue the line for the full 10 seconds. 1. 100 Speed (km/h) 75 50 25 0 1 2 3 4 5 6 7 8 9 10 Time (seconds) Directions: Answer each question or respond to each statement on the lines provided. 2. What is acceleration? 3. When a moving object reduces its speed, what happens to the object s acceleration in relation to its velocity? 4. Why is a car rounding a curve accelerating, even if it is moving at a constant speed? 5. What does each letter in the following equation stand for: a = (v f v i )/t? Describing Motion 51
Language Arts Support LESSON 3 Word-Usage Activity Parts of Speech All words can be categorized into parts of speech. Nouns, adjectives, verbs, and adverbs are parts of speech. A noun is a word that names a person, place, thing, or idea. An adjective is a word that describes a noun. A verb is an action word or a state-of-being word that tells about the subject. An adverb is a word that describes a verb, adjective, or another adverb. Directions: Circle the correct part of speech for each underlined term in the sentences below. 1. The average speed that people travel on highways has risen over the years. noun/verb/adjective/adverb 2. The teacher was constantly reminding the students that velocity is not the same as speed. noun/verb/adjective/adverb 3. If you walk from your home to your school, the initial location in your journey is your home. noun/verb/adjective/adverb 4. The acceleration of an object is defined as the object s change of velocity in a certain amount of time. noun/verb/adjective/adverb 5. To correctly state an object s velocity, you must specify a direction and a speed. noun/verb/adjective/adverb 6. When an object moves at a constant speed, its distance-time graph will be a straight line. noun/verb/adjective/adverb 52 Describing Motion
Language Arts Support LESSON 3 Sentence Structure Subjects and Predicates Sentences have subjects and predicates. Subjects can be nouns or pronouns that tell who or what the sentence is about. Predicates are the words that tell about the subject s action or its state of being. Predicates always have a verb. The particles subject Moving objects subject Tiny water droplets subject moved apart. predicate have kinetic energy. predicate rise into the air. predicate Remember that every sentence must contain a subject and predicate to be grammatically correct. Directions: Underline and label the subject and predicate in each sentence below. Underline the subject with one line. Underline the predicate with two lines. Study the example before you begin. Example: Constant speed means no speeding up or slowing down. 1. Instantaneous speed is the speed of an object at one instant in time. 2. Average speed is the total distance divided by the total time of movement. 3. The average speed equation contains variables for distance and time. 4. Velocity describes the speed and direction of an object. 5. Acceleration is a change in velocity. 6. A change in direction of a moving object is an acceleration. Describing Motion 53
Math Skills LESSON 3 Solve for Acceleration Acceleration is a measure of how much the velocity of an object changes in a unit of time. Acceleration is measured in units such as m/s 2. Acceleration is the change in velocity during a time interval divided by the time interval during which the velocity changes. This can be shown by the equation below, where a = acceleration, v f = final speed, v i = initial speed, and t = total time. a = (v f - v i ) t Pablo is running sprints. At 10 seconds, his speed is 2 m/s. At 20 seconds, his speed is 4 m/s. What was his acceleration during this time? To solve this problem, follow the steps below. Step 1 Identify the variables given in the problem. Subtract to find the time interval. v f = 4 m/s v i = 2 m/s t = 20 s - 10 s = 10 s Step 2 Substitute the known values to solve the equation. You are solving for a, the acceleration. a = (v f - v i ) t (4 m/s - 2 m/s) a = 10 s a = 0.2 m/s 2 Practice 1. After 30 s, a runner is sprinting at 3 m/s. But, 10 s later, the runner is sprinting at 3.8 m/s. What is the runner s acceleration during this time? 2. A car was moving at 14 m/s. After 30 s, its speed increased to 20 m/s. What was the acceleration during this time? 3. Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. What is her acceleration during this time? 4. Han s younger sister is riding her tricycle in a straight line. After 3 s, her speed is 0.5 m/s. After 5 s, her speed is 1.5 m/s. What is her acceleration during this time? 54 Describing Motion
School to Home LESSON 3 Acceleration Directions: Use your textbook to answer each question. 1. Speed, velocity, and acceleration describe how an object s position and motion change over time. What is acceleration, and what are two conditions that can change when an object accelerates? 2. Acceleration can be positive or negative. What type of motion would produce positive acceleration in an object? What type of motion would produce negative acceleration? 3. Acceleration of an object can be calculated if the initial speed, final speed, and total time the object is in motion are known. What is the acceleration of a car during a 5 minute interval in which it goes from 10 m/s to 15 m/s? 4. Motion can be described with speed-time graphs. How would a speed-time graph represent the motion of an object that is speeding up? How would it represent the motion of an object that is moving at a constant speed? Describing Motion 55
Key Concept Builder LESSON 3 Acceleration Key Concept What are three ways an object can accelerate? Directions: Put a check mark on the line before each motion listed below that involves an acceleration. 1. a car speeding up 2. a ball on the ground 3. a train going around a curve 4. a jet cruising on a straight path 5. the Moon orbiting Earth 6. a car stopping 7. a ball rolling down a ramp 8. a boat gliding toward a dock in calm water 9. a boat anchored in choppy water 10. a leaf falling from a tree 56 Describing Motion
Key Concept Builder LESSON 3 Acceleration Key Concept What are three ways an object can accelerate? Directions: The arrows on the right represent the accelerations of three objects that are speeding up (arrow pointing right) or slowing down (arrow pointing left). On the line before each motion, write the letter of the arrow that matches it correctly. 1. car pulling away from a traffic light 2. car slowing down for a stop sign 3. bullet being fired at a target 4. car stopping suddenly 5. jet taking off 6. bullet smashing into a target A. B. C. D. E. F. Directions: Answer each question on the lines provided. 7. The problems above involved changes in speed. How else can an object accelerate? 8. When a car goes around a curve at a constant speed, in which direction is it accelerating? Describing Motion 57
Key Concept Builder LESSON 3 Acceleration Key Concept What are three ways an object can accelerate? Directions: Answer each question or respond to each statement on the lines provided. 1. Kim and Julio go to a raceway to watch Julio s older brother, Raul, compete. Raul s car covers the 2.5 km in 12 seconds, reaching a speed of 180 km/h. Use the equation below to determine the rate of acceleration of Raul s car. In this equation, a is acceleration, v f is the final velocity, v i is the initial velocity, and t is time. (Hint: The initial velocity is 0 km/h.) a = (v f - v i ) t 2. In another race, Raul gets his car to go from a speed of 96 km/h to a speed of 240 km/h in 9 seconds. What was his acceleration? 58 Describing Motion
Key Concept Builder LESSON 3 Acceleration Key Concept What does a speed-time graph indicate about an object s motion? Directions: On the speed-time graph below, plot the speeds of three cars, as indicated. Label the lines you draw on your graphs car A, car B, and car C. 150 125 1 2 150 125 Speed (km/h) 100 75 50 Speed (km/h) 100 75 50 25 25 0 15 30 45 60 Time (seconds) 0 5 10 15 20 Time (seconds) 1. During a period of 60 seconds, car A travels at a speed of 125 km/h for 15 seconds and then slows to 100 km/h; car B travels at a speed of 75 km/h for 30 seconds and then increases to 125 km/h; car C travels at a constant speed of 50 km/h. Directions: Answer each question on the lines provided. 2. During a period of 20 seconds, car A slows at a constant rate from a speed of 100 km/h to a complete stop; car B travels at a constant speed of 50 km/h; and car C accelerates at a constant rate from a standstill to 100 km/h. 3. If a speed-time graph showing the motion of two cars contains two parallel horizontal lines, which line represents the faster car? 4. What does it mean if those two lines bend toward each other and meet at a point on the right side of the graph? 5. What is the limitation of speed-time graphs? Describing Motion 59
Enrichment LESSON 3 Amusement Park Physics Every year, scientists from NASA participate in Physics Day at amusement parks across the United States. The scientists work with students in grades K 12 to help them understand the physics of amusement park rides. Students really get into experiments when an amusement park is the laboratory, said Richard DeLombard, project manager for Exploration Outreach and Education at NASA s Glenn Research Center. It makes physics real to them. Roller Coasters On Physics Day, which usually takes place in the spring, DeLombard and his team use Cedar Point in Sandusky, Ohio, as their teaching laboratory. Students in the program go on roller coasters, among other rides. NASA scientists help the students relate their experience to that of astronauts. For example, as a roller coaster heads toward the bottom of a hill, the force of gravity and the cars acceleration press students back in their seats. For similar reasons, astronauts are pressed back in their seats during the launch of a spacecraft. Acceleration Patterns As part of Physics Day, students try to identify the acceleration patterns of different Applying Critical-Thinking Skills Directions: Answer each question or respond to each statement. rides. For example, at the beginning of a typical roller-coaster ride, the cars of the roller coaster are pulled by a chain to the top of a hill. Neither the speed nor the cars direction changes, so the cars have no acceleration. As the first car noses over the hill and begins to go down, acceleration increases slightly. Acceleration continues to increase with each car that crests the hill. It is highest when all the cars are streaking down the hill the steeper the hill is, the greater the acceleration will be. When the cars are evenly distributed at the bottom of the hill, there is a moment of zero acceleration. As the cars start over the next hill, acceleration does not spike again until the cars descend the hill. Fun with Physics Of course, most roller coasters are not made of simple hills and valleys. They have twisting loops and sharp turns with complicated acceleration patterns. The students who participate in Physics Day must pay close attention as they race upside down and sideways along the roller-coaster track. But the students don t seem to mind. As a NASA official point outs, learning really can be fun. 1. Determine whether a roller-coaster car has acceleration as it goes through a turn. Explain. 2. Give an Example In addition to a launch, where else might the astronauts feel the acceleration of their spacecraft? 60 Describing Motion
Challenge LESSON 3 Roller-Coaster Design Research roller-coaster designs. Then design a roller coaster in the space below. Include a brief explanation of your design. For example, explain why you placed hills, loops, or turns at certain points along your track. Be sure to consider the safety of riders, as well as general scientific principles. Describing Motion 61
Lab A 40 minutes Calculate Average Speed from a Graph You probably do not walk the same speed when you walk uphill versus downhill or when you are starting out versus when you are tired. If you are walking and you measure and record the distance you walk every minute, the distances will vary. How might you use these measurements to calculate the average speed you walked? One way is to organize the data on a distance-time graph. In this activity, you will use such a graph to compare average speeds of a ball on a track using different heights of a ramp. Ask a Question How does the height of a ramp affect the speed of a ball along a track? Materials metersticks (6) stopwatches (6) masking tape tennis ball Safety Make Observations 1. Read and complete a lab safety form. 2. Make a 3-m track. Place three metersticks end-to-end. Place three other metersticks end-to-end about 6 cm from the first set of metersticks. Use tape to hold the metersticks in place. Mark each half-meter with tape. Use books to make a ramp leading to the track. 3. A student should be at each half-meter mark with a stopwatch. Another student should be by the ramp to roll a ball along the track. 4. When the ball passes start, all group members should start their stopwatches. Each student should stop his or her stopwatch when the ball crosses the mark where the student is stationed. 5. Practice several times to get consistent rolls and times. Form a Hypothesis 6. Create a hypothesis about how the number of books used as a ramp affects the speed of the ball rolling along the track. 64 Describing Motion
Lab A continued Test Your Hypothesis 7. Write a plan for varying the number of books and making distance and time measurements. 8. Use the data table below to record your results. Add rows or columns if needed to match your plan. Distance (m) 0.50 1.00 1.50 2.00 2.50 3.00 Time (s) 2 books 3 books 4 books 9. Use your plan to make the measurements. Record them in the data table. 10. Plot the data for each height of the ramp on a graph that shows the distance the ball traveled on the x-axis and time on the y-axis. For each ramp height, draw a straight line that goes through the most points. Describing Motion 65
Lab A continued 11. Choose two points on each line. Calculate the average speed between these points by dividing the difference in the distances for the two points by the difference in the times. Remember to use scientific methods. Make Observations Ask a Question Form a Hypothesis Lab Tips If the ball doesn t roll far enough, reduce the track length to 2 m. Practice using the stopwatches several times to gain experience in making accurate readings. Test your Hypothesis Analyze and Conclude Communicate Results Analyze and Conclude 12. Compare the average speeds for each ramp height. Use this comparison to decide whether your hypothesis was correct. 13. The Big Idea How was the distance-time graph useful for describing the motion of the ball? Communicate Your Results Prepare a poster that shows your graph and describes how it can be used to calculate average speed. 66 Describing Motion
Lab B 40 minutes Calculate Average Speed from a Graph You probably do not walk the same speed uphill and downhill, or when you are just starting out and when you are tired. If you are walking and you measure and record the distance you walk every minute, the distances will vary. How might you use these measurements to calculate the average speed you walked? One way is to organize the data on a distance-time graph. In this activity, you will use such a graph to compare average speeds of a ball on a track using different heights of a ramp. Ask a Question How does the height of a ramp affect the speed of a ball along a track? Materials metersticks (6) stopwatches (6) masking tape tennis ball Safety Make Observations 1. Read and complete a lab safety form. 2. Make a 3-m track. Place three metersticks end-to-end. Place three other metersticks endto-end about 6 cm from the first set of metersticks. Use tape to hold the metersticks in place. Mark each half-meter with tape. Use books to make a ramp leading to the track. 3. A student should be at each half-meter mark with a stopwatch. Another student should be by the ramp to roll a ball along the track. 4. When the ball passes start, all group members should start their stopwatches. Each student should stop his or her stopwatch when the ball crosses the mark where the student is stationed. 5. Practice several times to get consistent rolls and times. Form a Hypothesis 6. Create a hypothesis about how the number of books used as a ramp affects the speed of the ball rolling along the track. Describing Motion 67
Lab B continued Test Your Hypothesis 7. Write a plan for varying the number of books and making distance and time measurements. 8. Use a data table that matches your plan. A table has been started below. Distance (m) Time (s) 9. Use your plan to make the measurements. Record them in the data table. 10. Plot the data for each height of the ramp on a graph that shows the distance the ball traveled on the x-axis and time on the y-axis. For each ramp height, draw a straight line that goes through the most points. 68 Describing Motion
Lab B continued 11. Choose two points on each line. Calculate the average speed between these points by dividing the difference in the distances for the two points by the difference in the times. Remember to use scientific methods. Make Observations Ask a Question Form a Hypothesis Lab Tips If the ball doesn t roll far enough, reduce the track length to 2 m. Practice using the stopwatches several times to gain experience in making accurate readings. Test your Hypothesis Analyze and Conclude Communicate Results Analyze and Conclude 12. Compare the average speeds for each ramp height. Use this comparison to decide whether your results support your hypothesis. 13. The Big Idea How was the distance-time graph useful for describing the motion of the ball? Communicate Your Results Prepare a poster that shows your graph and describes how it can be used to calculate average speed. Extension Design and conduct an experiment comparing the average speed of different types of balls along the track. Describing Motion 69
Lab C What Factors Affect Speed? Directions: Use the information and data from the Lab Calculate Average Speed from a Graph to perform this lab. You have done an experiment to determine how the height of a ramp affects the speed of a ball along a track. You timed balls as they rolled down different ramps and then recorded and graphed your data. What other factors aside from ramp height do you think could affect the speed of the ball? Some possibilities are size of the ball, the mass of the ball, the length of the ramp, and the shape of the ramp. Design a procedure to test a hypothesis about how changing a variable that is related to the balls or the ramp will affect the speed of the ball. As you design your experiment, be sure to control any other variables. Please note that you must complete Lab B before beginning Lab C. Also, have your teacher approve your design and safety procedures before beginning your experiment. 70 Describing Motion
Chapter Key Concepts Builder Describing Motion End-of-Chapter Practice Directions: Work with a partner. Select one of the options. When you have completed the tasks below, present your poster or graphs to the class. Use the space below to make notes and sketch drawings. 1. Choose ten objects that move at different speeds, from very slow to very fast, and learn about how much time it takes them to go a certain distance. Find a picture of each object and paste all the pictures to a large piece of poster board. Over each picture, draw a speedometer that is marked in appropriate units, showing the average speed of that object. 2. Choose ten modes of transportation that have been used from early times until today, such as horses and high-speed trains. Find out how long it takes for each kind of transportation to cover a certain distance 10 km, for example. Plot all ten modes of transportation as lines on a distance-time graph. Describing Motion 71