1. Chapter 3 Describing Motion

2. Chapter Objectives Describe a frame of reference Define and calculate average velocity Draw & interpret position vs. time graphs illustrating motion. Differentiate between vectors and scalars. Use average velocity equation to solve motion problems involving v, d and t Differentiate between average velocity and instantaneous velocity. Be able to determine the slope of a position- time graph and calculate velocity

4. What is motion? How do you know something is moving? What evidence do you need to be convinced that something is moving?

5. An object is moving if its position relative to a fixed point (reference point) is changing. 4.1 Motion Is Relative

6. Even things that appear to be at rest move. When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object. A book that is at rest, relative to the table it lies on, is moving at about 30 kilometers per second relative to the sun. The book moves even faster relative to the center of our galaxy. 4.1 Motion Is Relative

7. The racing cars in the Indy 500 move relative to the track. 4.1 Motion Is Relative

8. When we discuss the motion of something, we describe its motion relative to something else. The space shuttle moves at 8 kilometers per second relative to Earth below. A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track. Unless stated otherwise, the speeds of things in our environment are measured relative to the surface of Earth. 4.1 Motion Is Relative

9. Although you may be at rest relative to Earth’s surface, you’re moving about 100,000 km/h relative to the sun. 4.1 Motion Is Relative

10. think! A hungry mosquito sees you resting in a hammock in a 3- meters-per-second breeze. How fast and in what direction should the mosquito fly in order to hover above you for lunch? 4.1 Motion Is Relative

11. think! A hungry mosquito sees you resting in a hammock in a 3- meters-per-second breeze. How fast and in what direction should the mosquito fly in order to hover above you for lunch? Answer: The mosquito should fly toward you into the breeze. When above you it should fly at 3 meters per second in order to hover at rest above you. 4.1 Motion Is Relative

12. How can you tell if an object is moving? 4.1 Motion Is Relative

13. You can calculate the speed of an object by dividing the distance covered by time. 4.2 Speed

14. Before the time of Galileo, people described moving things as simply “slow” or “fast.” Such descriptions were vague. Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes. Speed is how fast an object is moving. 4.2 Speed

15. Any combination of units for distance and time that are useful and convenient are legitimate for describing speed: miles per hour (mi/h) kilometers per hour (km/h) centimeters per day light-years per century 4.2 Speed

16. A cheetah is the fastest land animal over distances less than 500 meters and can achieve peak speeds of 100 km/h. 4.2 Speed

17. We will primarily use the unit meters per second (m/s) for speed. If a cheetah covers 50 meters in a time of 2 seconds, its speed is 25 m/s. 4.2 Speed

19. Instantaneous Speed A car does not always move at the same speed. You can tell the speed of the car at any instant by looking at the car’s speedometer. The speed at any instant is called the instantaneous speed. 4.2 Speed

20. The speedometer gives readings of instantaneous speed in both mi/h and km/h. 4.2 Speed

21. Average Speed In a trip by car, the car will certainly not travel at the same speed all during the trip. The driver cares about the average speed for the trip as a whole. The average speed is the total distance covered divided by the time. 4.2 Speed

22. Average speed can be calculated easily: For example, a distance of 240 kilometers during a time of 4 hours is an average speed of 60 km/h: 4.2 Speed

23. The average speed is often quite different from the instantaneous speed. Whether we talk about average speed or instantaneous speed, we are talking about the rates at which distance is traveled. 4.2 Speed

24. If we know average speed and travel time, the distance traveled is easy to find. total distance covered = average speed × travel time For example, if your average speed is 80 kilometers per hour on a 4-hour trip, then you cover a total distance of 320 kilometers. 4.2 Speed

25. think! If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute? 4.2 Speed

26. think! If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute? Answer: In 10 s the cheetah will cover 250 m, and in 1 min (or 60 s) it will cover 1500 m. 4.2 Speed

27. think! The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later, what is the average speed? 4.2 Speed

28. think! The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later, what is the average speed? Answer: 4.2 Speed

29. How can you calculate speed? 4.2 Speed

30. Motion Diagrams What can you determine about the motion of the bird? The runner? The car?

31. A. Picturing Motion 1. Motion diagram - series of images of a moving object that records its position after equal time intervals – used to describe object at rest, in constant motion, accelerating, decelerating 2. Particle Model – a. replace object with a single point – b. point is usually center of mass of object – c. object is << than distance moved

32. Particle Diagram

33. B. Where and When 1. Coordinate System – a. tells you where the zero point is for the variable being studied – b. provides directions for increase/decrease 2. Position Vector – an arrow, showing magnitude and direction

34. Coordinate Systems Indicate direction

35. Distance vs. Displacement A jogger travels 2 km, stops to rest, then jogs back to his starting place. – What is the distance the jogger traveled? – What is his displacement?

36. b. Displacement(position) vs Distance (1) Displacement - separation, length and direction, from an object’s starting point and its final location – a vector quantity (2) Distance - how much, how large a separation exists – a scalar quantity, length of the arrow

37. Displacement ∆d = d f - d i

38. Motion Displacement is the distance and direction of an object's change in position from a reference point. Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark. The runner travels 50 m in the original direction (north) plus 30 m in the opposite direction (south), so the total distance she ran is 80 m.

39. Time Intervals ∆t

40. c. Time Interval – (1) t i, pronounced t initial, is used to describe time at start point – (2) t f would be the final time at end point – (3) change in a quantity is represented by the Greek letter delta,  (a) change is always final minus initial (b) change in time is,  t = t f - t i (c) change in displacement  d = d f - d i

41. What is the runners average velocity? _ V =  d/  t = 50m-0m/6s-0s = 50m/6s = 8.3 m/s

42. Position-Time Graphs

43. Position Time Graph A plot of displacement over period of time: Eq: d = v t, d is dependent, t is independent, v is constant What is the slope of this line? – slope = change in displacement over time – in other words - ??

44. Position vs. Time Graphs What does the slope of a position-time graph tell us? – The velocity – slope = m/s

45. – 1. When finding the slope use the largest possible triangle for greater precision – 2. The line goes through origin only if initial displacement was zero at time t = 0

46. Speed is a description of how fast an object moves; velocity is how fast and in what direction it moves. 4.3 Velocity

47. In physics, velocity is speed in a given direction. When we say a car travels at 60 km/h, we are specifying its speed. When we say a car moves at 60 km/h to the north, we are specifying its velocity. 4.3 Velocity

48. A quantity such as velocity that specifies direction as well as magnitude is called a vector quantity. Speed is a scalar quantity. Velocity, like displacement, is a vector quantity. 4.3 Velocity

49. Constant Velocity Constant speed means steady speed. Something with constant speed doesn’t speed up or slow down. Constant velocity means both constant speed and constant direction. Constant direction is a straight line, so constant velocity means motion in a straight line at constant speed. Can an object in orbit around the Earth be traveling at a constant velocity?? 4.3 Velocity

50. Changing Velocity If either the speed or the direction (or both) is changing, then the velocity is changing. Constant speed and constant velocity are not the same. A body may move at constant speed along a curved path but it does not move with constant velocity, because its direction is changing every instant. 4.3 Velocity

51. The car on the circular track may have a constant speed but not a constant velocity, because its direction of motion is changing every instant. 4.3 Velocity

52. think! The speedometer of a car moving northward reads 60 km/h. It passes another car that travels southward at 60 km/h. Do both cars have the same speed? Do they have the same velocity? 4.3 Velocity

53. think! The speedometer of a car moving northward reads 60 km/h. It passes another car that travels southward at 60 km/h. Do both cars have the same speed? Do they have the same velocity? Answer: Both cars have the same speed, but they have opposite velocities because they are moving in opposite directions. 4.3 Velocity

54. How is velocity different from speed? 4.3 Velocity

55. D. How Fast – 1. To describe motion you must specify its position. Do so by reference to a coordinate system with the origin as the starting point – Right + Up + – Left - Down - NOTE IT IS A VECTOR

56. 2. Average Velocity = change in displacement divided by time it took 3. Instantaneous Velocity – speed and direction at an instant in time - speed and velocity are not the same – speed is how fast, no direction

57. Motion Diagram Position-time Graph of Runners

58. d. Example - toy train A toy train moves along a straight line. Its position vs. time is shown the graph below. Avg vel for trip = avg vel for first 4 sec= avg vel for 2nd 4 sec= avg vel for 3rd 4 sec =

59. e. Example A high speed train takes 2.00 hours to travel 454 km from Paris to Lyons (due south). What is the average velocity in m/s? Given: d = 454 km, S t = 2.00 hr Find avg velocity 227 km/hr (1000 m/km)(1hr/3600sec) = 63.1 m/s, South

60. 2. Graph Considerations – a. Steep Slope - means high velocity – b. negative slope - moving in opposite direction (1) negative means a negative displacement (2) REMEMBER - ONE DIMENSIONAL – c. NOTE: for curved position vs time graphs the instantaneous velocity is the slope of a tangent to the graph at that point in time - will see this in next section

61. 3. Uniform Motion – a. equal displacements occur during successive equal time periods – b. straight lines on a position-time graph – c. slope of straight line is the uniform velocity

62. Speed vs. Velocity

63. Quantities Vectors – quantities that have magnitude and direction – Represented with arrows Scalars – quantities that have no direction

64. Adding Vectors Line up vector arrows from tip to tail Add magnitudes to find resultant vector

65. Subtracting Vectors Treat subtraction as addition of vectors with a negative sign

66. Instantaneous Velocity Speed and direction at a particular instant Speedometer How can we determine this on a position- time graph?

68. 4. If Paths A and B take the same time, then they have the same average velocity – but start end Path B Path A different speeds.

69. a. Displacement cannot be confused with distance traveled b. Average velocity cannot be confused with instantaneous velocity or with speed – (a) instantaneous velocity - velocity at a specified point in time – (b) speed is the magnitude of how fast

70. Objectives Plot and Interpret a velocity vs. time graph Understand the meaning of area under the curve on a velocity vs. time graph Calculate displacement from an velocity vs. time graph Define the concept of relative velocity

71. Displacement vs Distance - one more time – (1) displacement - how far from starting point and in what direction – (2) distance - how far you traveled – (3) both use ‘d’ or ‘s’ to represent them measured in meters distance is a scalar and displacement a vector

72. d. Confused Football Player Receives at his goal line Runs length of field in 11.5 seconds and, just before breaking the plane of the goal line, gets hit and confused and runs back to his starting point in 12.5 seconds. What was his average speed in ft/sec and his average velocity in ft/sec? (100 yds = 300ft) Ave. speed = 600ft/24s = 25 ft/s Ave. velocity = 0 ft/s why????

73. Relationships between v, d & t – average velocity = change in displacement / time – an average value - means some data points are more, others are less – if the average velocity is the same for all time intervals, you have CONSTANT or UNIFORM VELOCITY – A straight, sloped line on a position vs. time graph

74. Velocity Time Graphs Do not confuse with position-time graphs Plot velocity on the Y axis and time on the X axis At a constant velocity the plot is horizontal A straight sloping line = constant acceleration

75. Velocity Time Graphs Area under the line = the displacement For a constant velocity: d = vt *Note: It is the area of the rectangle under the line What is the displacement for the sloped line?

76. Relative Velocity A ship is moving forward at 10m/s. What are the velocities of a passenger on the ship relative to an observer sitting on the shore if: A.The passenger is walking towards the front at 2/s B.The passenger is walking towards the rear at 2 m/s C.Use vector addition: V o = V p + V s

77. Relative Velocity V o = V p + V s Scenario A: V o = +2 m/s + 10 m/s = 12 m/s Scenario B: V o = -2 m/s + 10 m/s = 8 m/s - 2 m/s+2 m/s +10 m/s

78. Relative Velocity