Position and Motion. Content Vocabulary LESSON 1. dimension displacement motion position reference point relative specify

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1 Content Vocabulary Position and Motion Directions: On each line, write the term from the word bank that correctly completes each sentence. NOTE: You may need to change a term to its plural form. dimension displacement motion position reference point relative specify 1. If you ask a friend to meet you somewhere, you will need to your location. LESSON 1 2. is the difference between the initial position and the final position of an object. 3. Your distance and direction from a reference point (for example, two blocks north of school) will define your. 4. Comparing your location to a starting point, or, helps describe where you are. 5. To describe the position of your school on a map, you need to describe its location in two. 6. The people on a bus are not moving in relation to the seats inside the bus, but they are in compared to the streets outside. 7. For the field trip, the buses will park three blocks east of the museum; this describes the position of the parking spot to the museum. Describing Motion 9

2 Content Practice A Position and Motion Directions: Complete this concept map by choosing terms from the word bank and writing them in the correct spaces. Each term is used only once. LESSON 1 difference direction displacement distance final initial reference point An object s 1. position is its 4. and is the from a between its and 7. positions Directions: On each line, write the term that correctly completes each sentence. 8. The terms and can be useful when giving opposite directions from a reference point. 9. The process of changing positions is. 10. is the length of a path taken, whereas is the difference between starting and ending locations.

3 Content Practice B Position and Motion Directions: Complete these paragraphs by writing the correct terms on the lines. Some terms might be used more than once. To describe an object s (1.), you must first choose a(n) (2.) as a starting place. From there, you must specify the (3.) to the object and the (4.) in which it lies from the starting place. If you are giving directions to two objects located LESSON 1 in different directions from the same (5.) be helpful to describe one object as being in the (6.) from that place and the other in the (7.), it can sometimes direction. direction An object is in (8.) any time its (9.) is changing. In most cases, such a change involves changes in (10.) and (11.) from the starting point. However, if an object returns to its starting point, its (12.) is zero, even though it might have traveled a considerable (13.). 14 Describing Motion

4 School to Home LESSON 1 Position and Motion For this activity, you will need the map below, a ruler, and a pencil. Refer to your textbook if you need help. 1. You are standing at the corner of River Street and Third Street. A friend calls and tells you to walk three blocks west of your present position to meet her. Where is your friend? What is the reference point for her directions? 2. Someone is standing at the southwest corner of Riverview Park. He wants to go to the post office by the shortest route. Write a set of directions for him. What distance will he walk? 3. Use a ruler and pencil to draw a line on the map that represents the displacement of the person who walked from Riverview Park to the post office in the question above. Without measuring, determine whether his distance walked and displacement are equal. Explain your answer. Describing Motion 15

5 Key Concept Builder Position and Motion LESSON 1 Key Concept What is the difference between distance and displacement? Directions: The diagram above represents an oval race-car track. Use the diagram to answer each question or respond to each statement. 1. When a race car reaches point B on the first lap, what is its distance traveled and its displacement? 2. When the car reaches point C on the first lap, what is its distance traveled and its displacement? 3. When the car reaches point D on the first lap, what is its distance traveled and its displacement? (Hint: Use a ruler.) 4. If a race is 10 laps, what is the car s distance traveled and its displacement when it reaches the finish line?

6 Lesson 1 Review LESSON 1 Position and Motion True or False Directions: On the line before each statement, write T if the statement is true or F if the statement is false. Matching 1. When you describe a position, you must only specify a distance. 2. Directing someone to walk north and west is describing a position in two dimensions. 3. Whether motion occurs depends on the reference point you use. 4. Displacement does not require movement. Directions: On the line before each definition, write the letter of the term that matches it correctly. Each term is used only once. 5. starting point describing the location of an object 6. the reference direction 7. direction opposite the reference direction A. positive direction B. negative direction C. reference point Multiple Choice Directions: On the line before each question, write the letter of the correct answer. 8. Which is a reference direction? A. faster B. the street C. to the north 9. Which statement indicates that motion has occurred? A. The reference point has changed. B. The position of the object has changed. C. The object being described has changed.

7 Content Practice A Speed and Velocity LESSON 2 Directions: On each line, write the term from the word bank that correctly completes each sentence. Each term is used only once. average constant direction distance horizontal instantaneous steep time velocity 1. Speed is a measure of the an object travels in a unit of. 2. When a moving object s change of position is equal in every second, it is moving at a(n) speed. 3. An object s speed at any particular moment is its speed. 4. Its speed for the entire duration that it is in motion from one place to another is its speed. 5. A(n) line on a distance-time graph shows a fast speed. 6. A(n) portion on a distance-time graph shows a period of no motion. 7. The of a moving object includes its speed and. 30 Describing Motion

8 Content Practice B Speed and Velocity Directions: Draw a line on each of the time-distance graphs below as instructed. LESSON 2 1. Show a car s constant speed of 75 km/h on a city street. 2. Show the motion of a car that travels for 30 seconds on a highway at a speed of 2 km/h, pulls off on the shoulder and stops for half a minute, and then resumes its trip at half its previous speed. Directions: Answer each question on the lines provided. 3. What is an object s velocity? 4. What are three ways that an object can change its velocity? Describing Motion 31

9 Math Skills Solve for Average Speed If a moving object changes speed, its average speed can be calculated. Average speed is the total distance traveled divided by the total time taken to travel that distance. This can be shown by the equation below, where v = average speed, d = distance, and t = time. LESSON 2 d v = t If Maria runs 6 km in 1.5 hours, what is her average speed? Step 1 Identify the variables given in the problem. d = 6 km t = 1.5 h Step 2 Substitute the known values to solve the equation. You are solving for v, the average speed. v v d = t 6km 1.5hours v = 4 km/h Practice 1. It takes Francisco 15 minutes to ride his bicycle 4 km, which is the distance from home to school. What is his average speed? 3. Byun walked 15 blocks in 25 minutes. What was his average speed? 2. Sara takes a 40-minute bus ride from her home to her grandparents home, which is 8 km away. What is the average speed of the bus? A bus trip covers 191 km and takes 4 hours and 15 minutes. What is the average speed of the bus in kilometers per hour? 32 Describing Motion

10 Date Class Key Concept Builder Speed and Velocity Key Concept What is speed? LESSON 2 Directions: The diagram shows the speedometers of the two cars, calibrated in kilometers per hour. Use the diagram to answer each question below. 1. What are the instantaneous speeds of car A and car B at the zero-second mark? 2. Counting from zero seconds, at what point will car B be going as fast as car A, if car B continues to gain speed at the same rate? 3. If car A keeps going at the same speed, how far will it travel in 2 hours? 4. If car B covers the same distance in 1.5 hours, what is its average speed? 34 Describing Motion

11 Key Concept Builder Speed and Velocity Key Concept How can you use a distance-time graph to calculate average speed? LESSON 2 Directions: Study the distance-time graph, showing the distances that eight different things cover in 120 seconds or less. The letters below correspond to the lines on the graph. On each line, write the correct average speed in meters per minute. A. bullet B. airplane C. car D. racehorse E. bike rider F. jogger G. hiker H. tortoise Describing Motion 35

12 Key Concept Builder Speed and Velocity Key Concept How can you use a distance-time graph to calculate average speed? LESSON 2 Directions: The distance-time graph above shows the varying speeds of a car, a train that stops at a station, and a roller coaster. Use the diagram to answer each question. 1. What is the average speed of the train (line A) in meters per second? 2. What is the car s average speed (line B) in meters per second? 3. What is the approximate maximum speed of the roller-coaster ride (line C) in meters per second? 4. What is the roller-coaster ride s average speed in meters per second? 5. About how long does the train sit at the station? 36 Describing Motion

13 Challenge Breaking the Record Before 1950, few people thought that a human could run a mile in under 4 minutes. Today, however, world-class runners routinely break the 4-minute-mile mark. The table shows the dates and the winning times for world-record mile runners. Dr. Trevor Kitson of Massey University in New Zealand studied data similar to these. He observed that the graph of the data was a straight line. From the graph, he predicted that the mile might be run in 3 minutes, 30 seconds, by the year Use the information in the table to create a graph similar to the one constructed by Kitson. Then extrapolate the data. Predict what will happen to the shape of the graph as time goes on. LESSON 2 Year Runner Mile Run Time (minutes:seconds) 1954 Roger Bannister 3: Jim Ryan 3: Steve Cram 3: Hicham El Guerrouj 3:43.13

14 Content Practice A Acceleration LESSON 3 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

15 Content Practice B Acceleration LESSON 3 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. 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 = (vf vi)/t? Describing Motion 51

16 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 v ) f t i 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 Practice Step 2 Substitute the known values to solve the equation. You are solving for a, the acceleration. ( vf vi) a t ( 4m s 2m s) a 10s a = 0.2 m/s 2 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? 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? 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? 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

17 Key Concept Builder Acceleration LESSON 3 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

18 Key Concept Builder Acceleration LESSON 3 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

19 Key Concept Builder Acceleration LESSON 3 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.) ( vf vi) a 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

20 Key Concept Builder Acceleration LESSON 3 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. 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. 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. Directions: Answer each question on the lines provided. 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

21 Lesson 3 Review Acceleration LESSON 3 True or False Directions: On the line before each statement, write T if the statement is true or F if the statement is false. Matching 1. Acceleration occurs when there is a change in speed. 2. When velocity decreases, velocity and acceleration arrows point in the same direction. 3. An object traveling at a constant speed is shown on a speed-time graph by a horizontal line. 4. Velocity cannot be represented by a speed-time graph. Directions: On the line before each definition, write the letter of the term that matches it correctly. Each term is used only once. 5. x-axis of a graph 6. final speed minus initial speed, divided by time 7. change in velocity during a period of time Multiple Choice Directions: On the line before each question, write the letter of the correct answer. A. acceleration B. vertical C. acceleration formula 8. Which situation would be indicated by an acceleration arrow and a final velocity arrow pointing in the same direction? A. an object speeding up B. an object at a standstill C. an object slowing down 9. Which direction would an acceleration arrow point when a bicycle is going around a curve? A. straight ahead B. toward the inside of the curve C. in the direction behind the bicycle

22 Velocity & Acceleration Graphs Name: 1. The graph to the right compares a. Distance and velocity b. Distance and time c. Speed and time d. Speed and distance 2. The vehicle is traveling fastest during trip portion a. A b. B c. C d. D 3. The distance traveled during trip portion B is a. 0 km b. 100 km c. 500 km d. 700 km 4. During trip portion B, the vehicle is a. Not moving b. Accelerating c. Decelerating 5. The distance traveled by the vehicle after 5 ½ hours is a. 100 km b. 500 km c. 600 km d. 700 km 6. The graph above compares &. 7. The car is accelerating during portions. 8. The car is decelerating during portions. 9. The car is not changing in velocity during portions.

23 Name: Date: Hour: MOTION REVIEW 1. How many meters can Swimmer 1 cover in 30 sec? 2. How far will Swimmer 2 go in 30 sec? 3. Predict the number of m Swimmer 1 can go in 60 sec. 4. Predict the number of m Swimmer 2 can go in 60 sec. 5. Which swimmer has the greatest speed? 6. Calculate the speed of Swimmer Calculate the speed of Swimmer 2. Short Answer Using complete sentences, discuss each of the following statements or questions. 1. In an amusement park you stand against the inside wall of a circular object that resembles a tin can. The circular object begins to whirl around. After a constant speed is reached, the floor drops down, but you are held fast against the whirling wall. Are you being accelerated? Explain your answer. 2. Explain why the slowing down of a moving object is considered to be a form of acceleration.

24 Indicate whether the following units represent distance (d), time (t), velocity (v), or acceleration (a) km m sec hours m/s cm/min/sec km/h cm/s m/s 2