Section Distance and displacment

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1 Chapter 11 Motion

2 Section 11.1 Distance and displacment

3 Choosing a Frame of Reference What is needed to describe motion completely? A frame of reference is a system of objects that are not moving with respect to one another. To describe motion accurately and completely, a frame of reference is necessary.

4 Learning Objectives a. Identify frames of reference and describe how they are used to measure motion. b. Identify appropriate SI units for measuring distance. c. Distinguish between distance and displacement. d. Calculate displacement using vector addition.

5 Choosing a Frame of Reference How Fast Are You Moving? How fast the passengers on a train are moving depends on the frame of reference chosen to measure their motion. Relative motion is movement in relation to a frame of reference. As the train moves past a platform, people standing on the platform will see those on the train speeding by. When the people on the train look at one another, they don t seem to be moving at all.

6 Choosing a Frame of Reference To someone riding on a speeding train, others on the train don t seem to be moving.

7 Choosing a Frame of Reference Which Frame Should You Choose? When you sit on a train and look out a window, a treetop may help you see how fast you are moving relative to the ground. If you get up and walk toward the rear of the train, looking at a seat or the floor shows how fast you are walking relative to the train. Choosing a meaningful frame of reference allows you to describe motion in a clear and relevant manner.

8 Measuring Distance How are distance and displacement different? Distance is the length of the path between two points. Displacement is the direction from the starting point and the length of a straight line from the starting point to the ending point.

9 Measuring Distance Distance is the length of a path between two points. When an object moves in a straight line, the distance is the length of the line connecting the object s starting point and its ending point. The SI unit for measuring distance is the meter (m). For very large distances, it is more common to make measurements in kilometers (km). Distances that are smaller than a meter are measured in centimeters (cm).

10 Measuring Displacements To describe an object s position relative to a given point, you need to know how far away and in what direction the object is from that point. Displacement provides this information.

11 Measuring Displacements Think about the motion of a roller coaster car. The length of the path along which the car has traveled is distance. Displacement is the direction from the starting point to the car and the length of the straight line between them. After completing a trip around the track, the car s displacement is zero.

12 Combining Displacements How do you add displacements? A vector is a quantity that has magnitude and direction. Add displacements using vector addition.

13 Combining Displacements Displacement is an example of a vector. The magnitude can be size, length, or amount. Arrows on a graph or map are used to represent vectors. The length of the arrow shows the magnitude of the vector. Vector addition is the combining of vector magnitudes and directions.

14 Combining Displacements Displacement Along a Straight Line When two displacements, represented by two vectors, have the same direction, you can add their magnitudes. If two displacements are in opposite directions, the magnitudes subtract from each other.

15 Combining Displacements A. Add the magnitudes of two displacement vectors that have the same direction. B. Two displacement vectors with opposite directions are subtracted from each other.

16 Combining Displacements Displacement That Isn t Along a Straight Path When two or more displacement vectors have different directions, they may be combined by graphing.

17 Combining Displacements Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy s home to his school is two blocks less than the distance he actually traveled.

18 Combining Displacements Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy s home to his school is two blocks less than the distance he actually traveled.

19 Combining Displacements Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy s home to his school is two blocks less than the distance he actually traveled.

20 Combining Displacements Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy s home to his school is two blocks less than the distance he actually traveled.

21 Combining Displacements Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy s home to his school is two blocks less than the distance he actually traveled.

22 Combining Displacements The boy walked a total distance of 7 blocks. This is the sum of the magnitudes of each vector along the path. The vector in red is called the resultant vector, which is the vector sum of two or more vectors. The resultant vector points directly from the starting point to the ending point.

23 Assessment Questions 1. A car is driving down the highway. From which frame of reference does it appear to not be moving? a. standing at the side of the road b. a car driving at the same speed but going the opposite direction c. sitting inside the car d. an airplane flying overhead

24 Assessment Questions 1. A car is driving down the highway. From which frame of reference does it appear to not be moving? a. standing at the side of the road b. a car driving at the same speed but going the opposite direction c. sitting inside the car d. an airplane flying overhead ANS: C

25 Assessment Questions 2. The SI unit of distance that would be most appropriate for measuring the distance between two cities is the a. meter. b. centimeter. c. kilometer. d. mile.

26 Assessment Questions 2. The SI unit of distance that would be most appropriate for measuring the distance between two cities is the a. meter. b. centimeter. c. kilometer. d. mile. ANS: C

27 Assessment Questions 3. If you walk across town, taking many turns, your displacement is the a. total distance that you traveled. b. distance and direction of a straight line from your starting point to your ending point. c. distance in a straight line from your starting point to your ending point. d. direction from your starting point to your ending point.

28 Assessment Questions 3. If you walk across town, taking many turns, your displacement is the a. total distance that you traveled. b. distance and direction of a straight line from your starting point to your ending point. c. distance in a straight line from your starting point to your ending point. d. direction from your starting point to your ending point. ANS: B

29 Assessment Questions 4. You travel 30 miles west of your home and then turn around and start going back home. After traveling 10 miles east, what is your displacement from your home? a. 20 km b. 20 km west c. 40 km d. 40 km west

30 Assessment Questions 4. You travel 30 miles west of your home and then turn around and start going back home. After traveling 10 miles east, what is your displacement from your home? a. 20 km b. 20 km west c. 40 km d. 40 km west ANS: B

31 Chapter 11.2 Speed

32 Learning Objectives Section 11.2 Identify the appropriate SI units for measuring speed. Compare and contrast average speed and instantaneous speed. Interpret distance-time graphs Calculate the speed of an object-using slope.

33 What is Speed? Speed is the ratio of the distance an object moves to the amount of time the object moves. Speed = Distance/Time The SI unit of speed is meters per second (m/s). Two ways to express the speed of an object are average speed and instantaneous speed.

34 Example Calculating Speed While traveling on vacation, you measure the times and distances traveled. You travel 35 kilometers in 0.4 hour, followed by 53 kilometers in 0.6 hour. What is your average speed? 1 st Get total distance 35 km + 53 km = 88 km 2 nd Get total time 0.4 hr hr = 1.0 hr.

35 Calculating Speed 3 rd - Plug and Chug Speed = Distance/Time Speed = 88 km / 1.0 hr. = 88 km/hr.

36 Now your turn A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1.0 kilometer in 16 minutes. What is the jogger s average speed in kilometers per minute? 1 st. Get total Distance 2 nd Get total Time 3 rd Plug and Chug into the Speed formula.

37 What is instantaneous speed? Sometimes you need to know how fast you are going at a particular moment. Instantaneous speed, v, is the rate at which an object is moving at a given moment in time.

38 Graphing Motion A distance-time graph is a good way to describe motion. Slope is the change in the vertical axis value divided by the change in the horizontal axis value. A steeper slope on a distance-time graph indicates a higher speed.

39 More Graphing motion

40 Chapter 11.2 Velocity & Vectors

41 Learning Objectives Section 11.2 Describe how velocities combine. Understand how speed and velocity are different

42 What is Velocity? Velocity is a description of both speed and direction of motion. Velocity is a vector. Sometimes knowing only the speed of an object isn t enough. You also need to know the direction of the object s motion. Together, the speed and direction in which an object is moving are called velocity Velocity = Change of Displacement/Time : ν = Δχ/t

43 Practice Problem #1 Karen walks 2.0 miles to the east in 45 minutes. What is her velocity in miles per hour? 1 st Define the variables X = 2 miles T = 45minutes =1 hour/60 minutes = 0.75 hours V =? 2 nd Determine Formula ν = Δχ/t 3 rd plug and chug 2 miles//.075 hours = 2.7 mph

44 Practice Problem #2 Heather and Matthew walk with an average velocity of 0.98 m/s eastward. If it takes them 34 min to walk to the store, what is their displacement? 1 st Define the variables V = 0.98 m/s eastward -> T 34 minutes (60 seconds/1 minute) = 2040 seconds X =? 2nd Formula (rearrange) V = x /t x vt 3 rd Plug and chug 0.98 m/s x 2040 seconds = meters (2.0 x 10 3 meters)

45 More Velocity Vectors can be used to show changes in motion. Vectors of varying lengths, each vector corresponding to the velocity at a particular instant, can represent motion. A longer vector represents a faster speed, and a shorter one a slower speed. Vectors point in different directions to represent direction at any moment.

46 Velocity As the sailboat s direction changes, its velocity also changes, even if its speed stays the same.

47 How to add velocities Sometimes the motion of an object involves more than one velocity. If a boat is moving on a flowing river, the velocity of the river relative to the riverbank and the velocity of the boat relative to the river combine. They yield the velocity of the boat relative to the riverbank. This is called relative velocity.

48 Combining Velocity The velocity of the boat relative to the riverbank is a combination of the relative velocities of the boat and the river.

49 Combining Velocity The velocity of the boat relative to the riverbank is a combination of the relative velocities of the boat and the river.

50 + Chapter 11.3 Acceleration

51 + Learning Objectives Section 11.3 Identify the change of motion that produces acceleration. Describe examples of constant acceleration Calculate the acceleration of an object. Interpret a speed-time and distance-time graph. Classify acceleration as positive or negative. Describe instantaneous acceleration.

52 + What is Acceleration? How does something accelerate? Basically it is the change of velocity with respect to time. Because it is the change of velocity and velocity is a vectors; that means acceleration is also a vector. Number and direction Ex: 20 m/s 2 east Speed Up (positive acceleration) Slow Down (negative acceleration) Change Direction Formula: a: acceleration v f : final velocity v i : initial velocity t: time

53 + Examples of Acceleration Change of Direction A horse on the carousel is traveling at a constant speed, but it is accelerating because its direction is constantly changing.

54 + More Examples of Acceleration Changes in Speed and Direction Sometimes motion is characterized by changes in both speed and direction at the same time. Passengers in a car moving along a winding road experience rapidly changing acceleration. The car may enter a long curve at the same time that it slows. The car is accelerating both because it is changing direction and because its speed is decreasing.

55 + Practice Problem #1 A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster s acceleration? GIVEN: WORK: v i = 10 m/s t = 3 s v f = 32 m/s a =? a = (v f - v i ) t a = (32m/s - 10m/s) (3s) a = 22 m/s 3 s a = 7.3 m/s 2

56 + Practice Problem # 2 How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s 2? GIVEN: t =? v i = 30 m/s v f = 0 m/s a = -3 m/s 2 WORK: t = (v f - v i ) a t = (0m/s-30m/s) (-3m/s 2 ) t = -30 m/s -3m/s 2 t = 10 s

57 Speed (m/s) + Graphing Motion - Acceleration Speed-Time Graph 3 2 slope = acceleration +vel = speeds up -vel = slows down 1 Straight Line = Constant Accel Flat Line = No Acceleration (0) Time (s)

58 Speed (m/s) + Graphing Motion Acceleration 3 Speed-Time Graph Specify the time period when the object was... 2 slowing down 5 to 10 seconds speeding up 0 to 3 seconds 1 moving at a constant speed 3 to 5 seconds Time (s) not moving 0 & 10 seconds

59 + Graphs of Accelerated Motion The skier s acceleration is positive. The acceleration is 4 m/s 2.

60 + Graphs of Accelerated Motion A distance-time graph of accelerated motion is a curve. The data in this graph are for a ball dropped from rest toward the ground. This means the ball is accelerating (speeding up)

61 + Free Fall Free fall is the movement of an object toward Earth solely because of gravity. Objects falling near Earth s surface accelerate downward at a rate of 9.8 m/s 2.

62 More on Free Fall Each second an object is in free fall, its velocity increases downward by 9.8 meters per second. The change in the stone s speed is 9.8 m/s 2, the acceleration due to gravity. t = 0 s v = 0 m/s t = 1 s v = 9.8 m/s t = 2 s v = 19.6 m/s t = 3 s v = 29.4 m/s

11.3 Acceleration The basketball constantly changes velocity as it rises and falls.

11.3 Acceleration The basketball constantly changes velocity as it rises and falls. The basketball constantly changes velocity as it rises and falls. Describing changes in velocity, and how fast they occur, is a part of describing motion. What Is Acceleration? How are changes in velocity