Representing Motion PDF

EXPLORATION 1 Representing Motion Imagine that you and a friend are planning to meet at the library. You want to meet at the library’s door, but you will travel to the library from different locations in the city....

EXPLORATION 1 Representing Motion Imagine that you and a friend are planning to meet at the library. You want to meet at the library’s door, but you will travel to the library from different locations in the city. FIGURE 1: A and B are starting positions of two friends on their way to the library. town hall door library A B Motion: Movement Displacement: Collaborate Change in distance Write a description and of the path to thedirection. door of the library starting from Velocity: Change in speed and direction. Position A in Figure 1 while a partner writes a description of the path starting from Position B. Magnitude: Value and follow your partner’s directions from your starting point. How does Trade descriptions, Scalar:theMagnitude. starting position Ex. affect Speed where you &endDirection. up? Vector: Magnitude and Direction. Ex. Velocity & Displacement. INFER Use evidence from your experience to infer what information scientists FIGURE 2: Two frames of need to include when communicating about position and motion. reference used to describe Note: When you write the speed you only write (Number) motion m/s, but when you write the velocity you write (number) m/ y-axis s Left/right/up/down. Same works for the distance and + displacement x-axis – + Frame of Reference Representations of motion, such as a multiple-exposure photo or a graph of © Houghton Mifflin Harcourt Publishing Company – position over time, enable scientists to quantify motion and look for patterns. a Cartesian Descriptions of motion should be accurate, and the usage of units should be consistent. Lack of precision can cause confusion. For example, the position North description “5 m” might mean a position “5 m above the floor” or a position “5 m left of the door.” Motion is a change in position relative to something else. Motion is described West East within a frame of reference, which is a system of coordinates that has a fixed origin. Figure 2 shows two common frames of reference that you might use to describe motion and position in science class or in everyday life. Examples South of origins might include things such as oneself, the steps in front of the local library, or the bottom left corner of a desk. The observed position and motion b Cardinal of an object depend on the frame of reference of the observer. 28 Unit 1 Physics and Engineering  Hands-On Lab Frame of Reference in Motion When police officers investigate car accidents, they may interview several FIGURE 3: Different witnesses. People watching from nearby sidewalks or other cars will make perspectives of the same car different observations of the motion of the cars in the accident. The officers must interpret each description based on frame of reference of that witness. In this activity, you will record the same event from various frames of reference, like the example in Figure 3. RESEARCH QUESTION How does frame of reference change the description of a moving object? a Car filmed from the side MAKE A CLAIM How does the location of a camera affect the way motion is captured? b Car filmed from behind POSSIBLE MATERIALS · meterstick · video-recording device, such · wind-up or remote- · tape as a cell phone control car SAFETY INFORMATION © Houghton Mifflin Harcourt Publishing Company Image Credits: ©HMH (both images) Wear safety goggles during the setup, hands-on, and takedown segments of the activity. If recording the car from above, make sure to attach the camera securely to its support. It should not be placed above shoulder height, and one student in the group should be on-hand to catch the assembly should it begin to fall. Immediately pick up any items dropped on the floor so they do not become a slip/fall hazard. PLAN THE INVESTIGATION In your Evidence Notebook, develop a procedure to investigate how frames of reference change how you describe the motion of the car. Make sure your teacher approves your procedure and safety plan before proceeding. When developing your procedure, consider the following: To compare the same event from different frames of reference, you will need to be able to recreate the car’s motion exactly in repeated trials. In some trials, the camera will be stationary. Adjust the car’s path and the camera’s position so that the path fits in the frame of the camera. In your plan, include a list of the camera shots that describes the position of the camera and the motion of the car. Also include a description of the camera’s motion if it moves during a shot. Plan to perform multiple trials of each shot. Lesson 2 Modeling Motion 29  ANALYZE 1. In your Evidence Notebook, draw the experimental setup for at least two of your trials. Label key components, and define your coordinate system. 2. When the camera is stationary, what determines the perceived direction of the car’s motion? 3. Suppose you film the car from the side. In one trial, the camera is moving at the same speed in the same direction as the car. In another trial, the camera is moving at the same speed in the opposite direction. If the car’s speed is 0.3 meters per second (m/s) relative to its surroundings, what will its apparent speed relative to the camera be in each trial? 4. How does the frame of reference affect how an observer perceives motion? In this lab, the camera is the observer, and the video recording is what an observer would perceive. DRAW CONCLUSIONS Write a conclusion that addresses each of the points below. Claim How does the location of the camera affect the way motion is captured? Was your initial claim correct? Evidence What evidence from your investigation supports your claim? © Houghton Mifflin Harcourt Publishing Company Reasoning Explain how the evidence you gave supports your claim. Describe in detail the connections between the evidence you cited and the argument you are making. Evidence Notebook How might viewing the beam prototypes in your unit project from different frames of reference yield information to help you improve the design? 30 Unit 1 Physics and Engineering  Position and Changes in Position If you were to describe your position, you may say “at my desk” or “by the teacher.” You would describe your position compared to some other point in space, like the desk or the teacher. In science, the point in space you refer to is the origin in a frame of reference. Modeling Changes in Position When something moves or is in motion, how it moves can be described with distance, direction, and time. Displacement is a change in position in a frame of reference that Displacement is the change is distance describes the distance and direction of an object’s final position from its initial position. and direction Examples of displacement include moving right 5 units on graph paper or walking 8 blocks north on a city grid. Quantities used to describe motion and other quantities in science are either scalars or vectors. A scalar is a quantity that has magnitude (duration or size) but no direction, such as 15 minutes (min) or 8.3 meters (m). A vector is a quantity that has both magnitude and direction, such as 14 centimeters (cm) forward, 0.09 millimeters per second (mm/s) left, or –15 m, where the negative sign indicates direction in a frame of reference. Vector variables are given in bold, for example v. A FIGURE 4: Vector representation of displacement, ∆x scalar that gives the magnitude of a vector but not the direction is indicated using absolute value notation as |v| or using scalar notation as v. Position is a vector 10 m 10 m 20 m 25 m 35 m because it has magnitude and direction from the origin in a frame of reference. Displacement, ∆x, is a vector that represents a change in the position vector x, as shown in Figure 4. The symbol ∆ is the Greek letter Delta, and it means change in. Distance is a scalar quantity. If an object travels in a straight path, the distance, how far it traveled, is the magnitude of its displacement, how much its position changed. For example, the displacement ∆x = –8 m corresponds to the distance of 8 m. In a 100 m race, runners travel a distance of 100 m, and the displacement is 100 m forward from the starting line. Vector quantities can be modeled with arrows. The length of the arrow corresponds to the magnitude of the vector, and the orientation of the arrow corresponds to its direction. FIGURE 5: Vector addition and subtraction in one dimension Vector Addition Vector Subtraction © Houghton Mifflin Harcourt Publishing Company A A B B A+B A + (–B) A+B=C A–B=C a  Vector addition for motion along b  Vector subtraction for motion along a straight line a straight line Arrow models of vectors can be helpful when adding and subtracting vectors, as shown in Figure 5. To add two vectors, align the head (triangle end) of the first arrow with the tail (flat end) of the second arrow. Draw a new arrow from the tail of the first arrow to the head of the second arrow. This new arrow represents the magnitude and direction of the resultant vector. Subtracting vectors is similar, except that you would align the subtracted arrow –B in the opposite direction as the original vector B. From there, subtraction is the addition of a negative term, so the head-tail method of vector addition can be applied. Lesson 2 Modeling Motion 31  Hands-On Activity Modeling Displacement The magnitude of displacement is sometimes but not always equal to the distance an object travels. In this activity, you will model a random path with a number line, a marker, and a coin. You will move the marker one unit with each coin flip, with the direction determined by the coin flip result. MATERIALS · safety goggles · coin · marker · number line SAFETY INFORMATION Wear safety goggles during the setup, hands-on, and takedown segments of the activity. Immediately pick up any items dropped on the floor so they do not become a slip/fall hazard. CARRY OUT THE INVESTIGATION Start the marker at zero on the number line, and flip the coin. For heads, move the marker one unit right; for tails, move one unit left. Conduct ten rounds of coin flips. In your Evidence Notebook, use vector arrow models to determine the displacement of your marker after ten coin flips. ANALYZE How does the distance traveled by the coin compare to its displacement after ten flips? Compare your results with those of other groups. Changes in Position over Time © Houghton Mifflin Harcourt Publishing Company Image Credits: ©HMH Velocity is the change in speed The velocity of an object is a vector giving its speed in a particular direction. The average V-avg = and direction velocity over a time interval is the displacement of the object divided by that time interval. Displacement / Time ANNOTATE A sprinter is photographed at equal time intervals. Draw vectors arrows to indicate the displacement between adjacent images of the sprinter. What happens to the sprinter’s displacement between images? What happens to the sprinter’s velocity? 32 Unit 1 Physics and Engineering  Math Connection Average and Instantaneous Velocity A dog runs across a field in a straight line, and its motion can be analyzed with a position-time graph (Figure 6). The x-axis shows time, t; the y-axis shows position, x. The change in the y-value between any two points gives the dog’s displacement over that time interval. Dividing the change in y (position) by the change in x (time) will give the average velocity in that interval. Place a straight edge between the points for t = 0 s and t = 4 s in Figure 6. The slope of the line (rise ÷ run) is equal to the runner’s average velocity during that segment. displacement ​x​  final​–​x​  initial​ ∆x average velocity = ​​ __    ​​  =  ​​ _     ​​ = ​​ _ ​​ change in time t​ ​  final​–​t​  initial​ ∆t To find the average velocity in the first 4 s, and over the whole graph: 20 m − 0 m v = ​​  _  ​​  = 5 m/s forward 4s−0s 100 m − 0 m v = ​​  __  ​​  = 10 m/s forward 10 s − 0 s Over the entire 100 m, the average velocity was 10 m/s forward, but this number does not capture Position-Time Graph of a Running Dog the velocity at each point in the dog’s path. The FIGURE 6: The position of a dog at 2 s intervals average velocity in the first 2 s was slower, and 100 the average velocity in the last 2 s was faster. The average velocity only conveys the total motion over 80 that interval, not the precise velocity at any single Position (m) moment. The dog’s momentary velocity at one 60 point in time is called the instantaneous velocity. 40 If the graph were a straight line, it would indicate that displacement changed linearly over time, and 20 so velocity was constant. That velocity would be 0 equal to the slope of the line. A curved line on a 0 2 4 6 8 10 position-time graph indicates that the velocity is Time (s) changing over time. EVALUATE Determine whether the question asks © Houghton Mifflin Harcourt Publishing Company Average Instantaneous about an average or instantaneous velocity. velocity velocity How fast must you bike to get there in half an hour? What is the fastest she can run? What is the minimum speed for takeoff? How fast did he run the first 5 miles of the marathon? Evidence Notebook Look back at the multiple-exposure photo of the sprinter as well as the position versus time graph for the dog in Figure 6. If the sprinter and dog were instead slowing down, how would the photo and graph look different? Lesson 2 Modeling Motion 33  What is the distance traveled? The distance traveled is 12m + 15m + 18m = 45m. What is the displacement? The displacement is 0 meters. (∆x) (m) (∆t) (s) To find on graphs: = ∆𝑥 𝑥2 −𝑥1 m/s ∆𝑡 = 𝑡2 − 𝑡1 What is the displacement? The displacement is 270 meters. What is the time? The time is 60 seconds. What is the average speed? 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 270𝑚 Average Speed = = = 4.5 m/s 𝑇𝑖𝑚𝑒 60𝑠 What is the average velocity? 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 270𝑚 Average Speed = = = 4.5 m/s 𝑇𝑖𝑚𝑒 60𝑠 EXPLORATION 2 Acceleration in One Dimension One-dimensional motion is motion along a straight line. A rising elevator, a container lifted by a crane, and the ball in Figure 7 are examples of objects in one-dimensional vertical motion. A moving train car, a person walking down a hallway, and the ball in Figure 8 are examples of objects in one-dimensional horizontal motion. FIGURE 7: A ball FIGURE 8: A ball rolls across a table. falls freely. Patterns Patterns in Motion Throughout your experiences, you observe many different patterns in motion. You may observe patterns in speed: some objects speed up, some objects slow down, and still other objects move at constant speeds. You may also observe patterns in direction of motion: some objects move in straight lines, some move in circles, and some follow other paths. EVALUATE For the images in Figure 7 and Figure 8, the balls were photographed at © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Richard Megna/Fundamental equal time intervals. What patterns do you see in the motions of the two balls? How are their motions different? Changes in Velocity For an object in motion, the object’s position is always changing, and its velocity can also Acceleration is the change. Acceleration is a change in velocity over time. Like displacement and velocity, rate of change of acceleration is a vector quantity because it has magnitude and direction. When the Photographs velocity acceleration of an object is in the direction of motion, the object speeds up. When the acceleration is in the opposite direction, the object slows down. Acceleration is the rate of change of velocity, ∆ ​ /​∆t​. ​ v ​v​  final​–​v​  initial​ _ ​v​  f​–​v​  i​ _ ∆v a =_ ​ ​​t​  ​–​t​   ​​​ = ​​  ​t​  ​–​t​   ​​​ = ​​  ​​ final initial f i ∆t 34 Unit 1 Physics and Engineering  Horizontal Motion Suppose a ball rolls to the right, moving at constant velocity. The ball hits a spring, and the ball slows as the spring compresses. The ball comes to rest and then accelerates to the left as the spring expands. In this frame of reference, right is defined as the positive direction. ANALYZE Use the models in Figures 9 and 10 to complete the table. Use only +, –, and 0 to indicate whether the quantity is positive, negative, or zero at that time. FIGURE 9: The ball’s speed decreases as the spring Time, t Position, x Velocity, v Acceleration, a compresses, indicating acceleration opposite to 0s 0 cm + 0 the direction of motion. As the spring expands, it accelerates the ball to the left. 1s 20 cm + 0 a=0 2s 40 cm + 0 t=0 v 3s 57 cm + - a=0 4s 67 cm 0 - t=1 v 57 cm - - 5s a=0 - 0 t=2 v 6s 40 cm 7s 20 cm - 0 a t=3 v 8s 0 cm - 0 a FIGURE 10: The graph shows the position of the ball t=4 over time. Where the slope is changing, the velocity is changing. a v 80 t=5 70 va=0 60 Position (cm) t=6 50 40 va=0 30 t=7 20 10 va=0 t=8 0 © Houghton Mifflin Harcourt Publishing Company 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 Position (cm) Time (s) EXPLAIN Describe the acceleration of the ball before, during, and after hitting the spring. How does the spring affect the velocity and acceleration of the ball? If the spring were removed, the ball would continue moving to the right without slowing, speeding up, or changing direction. This uniform motion would look the same as the motion in Figure 8. Because the ball’s displacement would be equal in equal time intervals, its velocity would be constant, and its acceleration would be zero. Lesson 2 Modeling Motion 35  Vertical Motion Suppose that a ball is dropped and falls freely as it is accelerated by gravity. The magnitude of acceleration due to gravity is 9.8 meters per second squared (m/s2) for a freely falling object near Earth’s surface. When the ball hits a spring, the spring slows it until it stops. The spring then pushes upward on the ball until the ball is launched back into the air. ANALYZE Use the models in Figures 11 and 12 to complete the table. Use only +, –, and 0 to indicate whether the quantity is positive, negative, or zero at that time. In this frame of reference, downward is defined as the negative direction. FIGURE 11: A ball is held at 60 cm and then dropped onto a spring, compressing the spring. The spring then expands, pushing up on the ball and launching it into the air. 80 70 60 a v a a Position (cm) 50 v v 40 a a 30 v v a a 20 a v 10 0 t=0s t = 0.1 s t = 0.2 s t = 0.3 s t = 0.4 s t = 0.5 s t = 0.6 s t = 0.7 s Time, t Position, x Velocity, v Acceleration, a FIGURE 12: The graph shows the position of the ball over time. Where the slope is changing, the velocity 0s 60 cm 0 –9.8 m/s2 is changing. 0.1 s 55 cm - –9.8 m/s2 70 60 0.2 s 40 cm - –9.8 m/s2 50 Position (cm) 0.3 s 22 cm - + 40 0.4 s 14 cm 0 + 30 22 cm + 20 0.5 s + 10 0.6 s 40 cm + –9.8 m/s2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 © Houghton Mifflin Harcourt Publishing Company 0.7 s 55 cm + –9.8 m/s 2 Time (s) EXPLAIN Order the list to describe the ball’s motion as it drops onto the spring. 4 a. The acceleration of the ball decreases as the spring extends. 3 b. The push from the spring exceeds the pull of gravity. The ball momentarily comes to rest. 6 c. The velocity decreases due to gravitational acceleration in the negative direction. 2 d. Acceleration of the ball changes directions from negative to positive due to an upward push from the spring. 1 e. The ball is dropped from rest and then accelerates in the negative direction. 5 f. The ball leaves the spring with a large velocity in the positive direction. The acceleration due to gravity is in the negative direction. 36 Unit 1 Physics and Engineering  An object is said to be in free fall when gravity is the only force acting on it. Near Earth’s surface, objects in free fall have a constant acceleration downward. Because downward is usually defined as the negative direction, acceleration due to gravity is often shown with a negative sign. For an object in free fall, the vertical component of the object’s motion exhibits constant acceleration and thus a changing velocity. Rising objects have a velocity in the positive direction that is decreased by gravity over time, and falling objects have a velocity in the negative direction that is increased by gravity over time. Hands-On Activity Falling Objects In this activity, you will explore the effect of mass on the acceleration of falling objects. MATERIALS safety goggles · two or more objects of different masses SAFETY INFORMATION Wear safety goggles during the setup, hands-on, and takedown segments of the activity. Immediately pick up any items dropped on the floor so they do not become a slip/fall hazard. CARRY OUT THE INVESTIGATION Align the bottoms of two objects that have different masses and drop them. Do they hit the ground at about the same time, or at different times? Repeat several times with different objects and from different starting heights. In your Evidence Notebook, describe what happened in terms of the objects’ masses. Does more mass make an object hit the ground first, or does mass have no effect? ANALYZE In a vacuum chamber with no air resistance, would a feather and hammer dropped from the same height hit the ground at the same time? Explain your reasoning with evidence from your investigation. © Houghton Mifflin Harcourt Publishing Company Evidence Notebook Compare the motion of the ball falling and rolling horizontally in Figures 7 and 8 with the motion of the skier. Describe the velocity and acceleration of each ball and of the skier. Define up and right as positive. Lesson 2 Modeling Motion 37 Accelaration in One Dimention BY M R. MO HA MM A D A L KH AT I B  Unit 1 Lesson 2 Acceleration in One Dimension Patterns A ball rolls across a table. A ball falls freely. Balls were photographed at equal time intervals to produce the Falling Ball and Rolling Ball photos. What patterns do you see in the motions of the two balls? How are their motions different? 2 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 3 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 4  Text Text Text 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 5  Unit 1 Lesson 2 Acceleration in One Dimension Example : For an object in motion, the object's position is always changing, and its You are stopped at a red light. When it turn green, you speed velocity can also change. up 45m/s. that is your change in velocity? Acceleration is a change in velocity V = Vf - Vi over time. Like displacement and Vi = 0 m/s velocity, acceleration is a vector Vf = 45 m/s V = 45 - 0 2 quantity because it has magnitude V= 45 m/s and direction. What if he used 5s ? Acceleration is the rate of change of velocity. Vi = 0 m/s V = Vf - Vi V = V / time Vf = 45 m/s V = 45 - 0 V = 45 / 5 2 V= 45 m/s V = 9 m/s 6  What is negative acceleration? - Also know as DECELERATION. - The negative rate of change of velocity. - The amount of negative change of velocity in a time interval. - Slowing down. 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 7 Unit of Accelaration Other Units : Km/hr, miles/hr ,ft/s To change from km/h to m/s: Speed and velocity are easily measured in distance/time units, such as Km/hr, 10 km/h = 10/3.6 m/s m/s. 20 km/h = 20/3.6 m/s 9 km/h = 9/3.6 m/s Acceleration considers: velocity unit/time unit 𝒎/𝒔𝟐 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 8  Acceleration in One Dimension- Horizontal Motion Horizontal Ball and Spring | The ball's speed decreases as the spring compresses, indicating acceleration opposite to the direction of motion. As the spring expands, it accelerates the ball to the left. 1 1/ 18 /2 0 24 Solve the Example in the Book 9  Unit 1 Lesson 2 Acceleration in One Dimension- Vertical Motion A ball is held at 60 cm and then dropped onto a spring, compressing the spring. The spring then expands, pushing up on the ball and launching it into the air. 10 Solve the Example in the Book  Problems 1. How much time does a car with an acceleration of 2 𝑚/𝑠 2 take to go from 15 m/s to 30 m/s? 2. What is the acceleration if we speed up from 10 km/h north to 30 km/h in 10 seconds? 3. What is the final velocity of a car starting at rest and that accelerates at a rate of 40 𝑚/𝑠 2 in 10 seconds? 4. Omar 'struck decelerates from 72 m/s to 0 m/s in 6 seconds. What is his rate of deceleration? 5. A ball is dropped from rest and falls freely under the influence of gravity. If it accelerates at g= - 9.81 𝑚/𝑠 2 for 5 seconds, what is the final velocity of the ball just before it hits the ground? 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 11  v a t 1 1/ 18 /2 0 24 SAMPL E FOOTER TEXT 12 Physics Unit 1: Physics and Engineering Lesson 2: Modeling Motion Exploration 1 Representing Motion  Unit 1 Lesson 2 Can You Solve the Problem? PREDICT This multiple- exposure photo does not show the skier's full jump. What do you think happens to the skier in the rest of the jump? 2  Unit 1 Lesson 2 Representing Motion COLLABORATE Using the Street Map, write a description of the path to the door of the library starting from Position A while a partner writes a description of the path starting from Position B. Trade descriptions, and follow your partner's directions from your starting point. How does the starting position affect where you end up? 3  Unit 1 Lesson 2 Representing Motion Motion is a change in position relative to something else. Motion is described within a frame of reference, which is a system of coordinates that has a fixed origin. 4 Distance vs Displacment Distance : The total length of the path traveled, regardless of direction. Unit ? Scalar or Vector Displacement : The shortest straight-line distance from the starting point to the ending point, along with the direction Unit ? Scalar or Vector ? 5  Unit 1 Lesson 2 Representing Motion ANALYZE What happens to the sprinter's displacement between images? What happens to the sprinter's velocity? 6 7 8 9 10  Unit 1 Lesson 2 Representing Motion 11 12 13 Average velocity vs instantaneous velocity Solve thePosition-Time Graph of a Running Dog Example in the Book 14 Name:_____________________________________________Date:_______________ _____________ The velocity-time graph below shows the run of a sprinter. a. Use the graph to estimate the sprinter’s speed after 8 seconds. 4 m/s b. During which period was the sprinter’s speed constant? 20s - 30s c. What was the sprinter’s maximum speed? 10 m/s  d. Use the graph to find the sprinter’s acceleration between 0 and 20 seconds. a = Vf-Vi / t = 10 - 20 / 20 = 10 / 20 = 0.5 m/s ^ 2 e. Calculate the car’s deceleration between 30 and 60 seconds a = Vf-Vi / t = 10 - 0 / 60 - 30 = 10 / 30 = 0.33 m/s ^ 2 f. Find the area between 𝑡 = 0𝑠 𝑎𝑛𝑑 𝑡 = 20𝑠 Area = b x h / 2 A = 20 x 10 / 2 A = 200 / 2 A = 100 m ^ 2 Number 1: Define the following terms: a) Distance: Is the total length of the path traveled by an object b) Displacement: Is the change in distance and direction Number 2: 1km A car is moving from A to B, from B to C, from C to D, from D to E, from E to F. Calculate the distance and the displacement of the car. Distance: 13 KM Displacement: 4 KM 2 Number 3: Station C Station D Station E A train is travelling from station A to station C, from station C to station D, from station D to station E, and stops at station B. 750 km a) Find the distance travelled by the train. b) Find the displacement of the train. 400 km Number 4: 120 km 320 km 3 Number 5: An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure below. a) Find the distance covered by the moving object. 17 km b) Find the magnitude and direction of the displacement of the object. 9 km right Number 6: A boy starts its ride from point A, passes by B, then from B to C and stops at A. a) Determine the distance travelled by the boy b) Determine its displacement 12 m 0 m, he went back 4 Number 1: A football field is about 100 meters long. If it took Fahad 20 seconds to run its length, how fast was he running? S avg = distance / time = 100 / 20 = 5 m/s Number 2: A person walks 60 meters in 60 seconds; then walks 30 meters in 120 seconds. What is his average speed? Total distance = 60 m + 30 m = 90 m Total time = 60 s + 120 s = 180 s Average speed = 90 m ÷ 180 s = 0.5 m/s Number 3: v v The distance from Rima’s home to her grandparent’s house is 50 km. Every weekend, Rima takes 2 hours to reach their house by car. 1. Find the speed of the car. 2. Find the velocity of the car. 1. S = distance / time = 50 / 2 = 25 km/h 2. V = displacement / time = 50 / 2 = 25 km/h right 2  Number 4: Hannah leaves her house to go to the library. She walks 400m east along East Street in 400 seconds and then 300m north along North Street in 400 s to reach the library. 1. Calculate the velocity of Hannah along East Street. 2. Calculate the speed of Hannah along the entire path. 1. V = displacement / time = 400 / 400 = 1 m/s east 2. Total Time: 400 + 400 = 800s Total distance: 400 + 300 = 700 m Speed = distance / time = 700 / 800 = 0.875 m/s 3 Number 5: A biker moves from point A then pass by point B, than C then go back to A. It took him 100 s to complete his path. 1. Calculate the average speed of the biker. 2. Calculate the velocity of the biker during his race. 1. Total Distance: 4 + 3 + 5 = 12 m Total time: 100s Speed = distance / time = 12 / 100 = 0.12 m/s 2. V = Displacement / time = 0 / 100 = 0 m/s 4