1. Motion of an object is described by its position, speed, direction, and acceleration.

2) MKS units are Meters, Kilograms Seconds

3. Initial means “first” or “starting”

4 . D = “delta” D means “the change in” 5. D= final – initial

6. wrt means “with respect to”

7. fixed means constant, unchanging.

When is an object moving?

4.1 Motion Is Relative 8. An object is moving when its position changes relative to a fixed point.

Vectors and Scalars

4.1 Motion Is Relative 9 . Vectors or vector quantities have magnitude and direction Scalars or scalar quantities have only magnitude

11. Magnitude means size

4.1 Motion Is Relative 12. Distance means total path length an object travels 13.Displacement means final position minus initial position

4.1 Motion Is Relative 14. In symbols Displacement = Dx or Dy

Travel around perimeter:

Travel around perimeter: from A B

Travel around perimeter: from A BC

Travel around perimeter: from A BC D

Travel around perimeter: from A BCDA

Distance = path length =

Distance = path length =28 m

Distance = path length =28 m Displacment = 0

15) Distance is a scalar and Displacement is a vector

16. Motion is relative: we always describe motion relative to something else

17. Usually we measure motion relative Earth’s surface

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

http://www. youtube. com/watch. v=oRBchZLkQR0 http://www. youtube http://www.youtube.com/watch?v=oRBchZLkQR0 http://www.youtube.com/watch?v=KLd-rJMoeko http://www.youtube.com/watch?v=xMF2CfYLomY

4.2 Speed 18. Speed = distance time v = d t

people described motion as “slow” or “fast.” 4.2 Speed 19. Before Galileo, people described motion as “slow” or “fast.”

20.Galileo was the first to calculate speed 21. Speed is how fast an object moves

4.2 Speed 22. MKS units of speed meters/second = m/sec . v = d t

4.2 Speed

23. Instantaneous speed is the speed at an instant of time 24. Speedometer measures instantaneous speed.

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

= total distance total time. 4.2 Speed Average Speed 25. average speed = total distance total time.

Is average speed the same as instantaneous speed?

26. HOW FAR: total distance d = average speed X total time d = v • t REARRANGE equation: v = d/t 26. HOW FAR: total distance d = average speed X total time d = v • t

27. Odometer measures how far an object travels.

4.2 Speed How can you calculate speed?

28. Velocity is speed in a specific direction.

29. MKS units of Velocity : m/sec

the rate of change of position V = Dx Dt 4.3 Velocity 30. Velocity is the rate of change of position V = Dx Dt

31. Rate always means wrt time 4.3 Velocity 31. Rate always means wrt time

and Velocity is a vector. 32. Speed is a scalar; and Velocity is a vector.

at constant speed. 4.3 Velocity Constant Velocity 33. Constant velocity means traveling in a straight line at constant speed.

34. Velocity changes if speed changes or direction changes Changing Velocity 34. Velocity changes if speed changes or direction changes or both change .

4.3 Velocity 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 How is velocity different from speed?

35. Acceleration = change in velocity time interval a = DV DT

36. Acceleration is the rate of change of velocity.

37. Acceleration means decreases or increases in velocity. 38. Decreased acceleration is called deceleration.

37. Acceleration means decreases OR increases in velocity. 38. Deceleration = decreased acceleration The brakes of a car cause deceleration.

a vector quantity because it depends on direction 4.4 Acceleration Change in Direction 39 . Acceleration is a vector quantity because it depends on direction

4.4 Acceleration Change in Direction 40. REMEMBER Speed and velocity are NOT the same. Acceleration is the rate of change of velocity, NOT speed. Acceleration is a vector quantity because it has direction .

vectors: 41. Speed up: Accelerate in the same direction as velocity

4.4 Acceleration 41. Speed up: Accelerate in the direction of velocity 42. Slow down: Accelerate against direction of velocity

4.4 Acceleration 41. Speed up: Accelerate in the direction of velocity 42. Slow down: Accelerate against velocity 43: Change direction: Accelerate at an angle to velocity

4.4 Acceleration Velocity units: meters/second = m/sec 44. MKS Acceleration units : meters/second = m/sec2 second

4.4 Acceleration How do you calculate acceleration?

45. Free fall assumptions: A) no air resistance B) only gravity force affects motion of object

46. Projectile = Object in free fall 47 46. Projectile = Object in free fall 47. Trajectory = path of projectile

48. Time t is the time elapsed since projectile began to move. 4.5 Free Fall: How Fast Falling Objects 48. Time t is the time elapsed since projectile began to move.

4.5 Free Fall: How Fast 49. Every second of free fall: instantaneous speed of object increases by ~ 10m /sec . V = 10 t

50. Acceleration of free fall =g g  10 m sec2

51. g is “acceleration due to gravity” 52. g is NOT called “gravity”

53. For more precise calculations use g = 9.8 m/sec2

4.5 Free Fall: How Fast 54. HOW FAST: Instantaneous speed in free fall v = gt v = 10 t

4.5 Free Fall: How Fast

4.5 Free Fall: How Fast 55. Average projectile speed = Vavg Vavg = initial speed + final speed 2 Vavg = Vf + Vi

4.5 Free Fall: How Fast Rising Objects 56. A projectile thrown straight up: slows as it travels up . stops momentarily free falls back down

4.5 projectile moving straight up 57. When projectile travels up: a) Velocity is ↑ acceleration= g ↓ b) Velocity DECREASES 10 m/sec every second

4.5 projectile moving straight up: 58. At highest point in trajectory, velocity = 0 acceleration = g↓.

4.5 projectile moving straight up: 59. when traveling back down, a) velocity ↓ ; acceleration =g ↓ . b) velocity increases in 10 m/sec ↓every second

4.5 Free Fall: How Fast 60. The change in speed in each second is the same going up or down

4.5 Free Fall: How Fast What is the acceleration of an object in free fall?

4.6 Free Fall: How Far 61. Every second in free fall, a projectile falls further than it did the previous second.

d =½ gt2 = ½ [10]t2 =5 t2 d = 5t2 4.6 Free Fall: How Far 62. HOW FAR: distance a projectile free falls : d =½ gt2 = ½ [10]t2 =5 t2 d = 5t2

4.6 Free Fall: How Far

63. Galileo derived these kinematics equations experimentally v = at = 10 t and d = ½ at2 = 5t2

64. Summary free fall on Earth a = g= 10 m/sec2 how fast: v = at = 10 t how far: d = ½ at2 = 5t2

4.6 Free Fall: How Far For a falling object, how does the distance per second change?

4.7 Graphs of Motion 65. Graphs visually describe relationships.

66. In motion graphs, time is ALWAYS on the x-axis

4.7 Graphs of Motion graphing free fall 67. On a speed-versus-time graph [v-t graph] the slope represents acceleration. 68. On a v-t graph, the area under the curve equals the total distance traveled.

V-t graph: slope = acceleration

V-t graph: area under curve = displacement

V-t graph: area under curve = displacement Area of triangle = ½ b h

area under curve: =½ base X height =½ [5 sec][50 m/sec]

area under curve: =½ base X height =½ [5 sec][50 m/sec] = 125 m

V-T graph 69. linear relationship = straight line on v-t graph time and velocity are directly proportional 70. slope on v-t graph is constant 71. If t doubled , then v doubled

72. Displacement-Versus-Time in free fall d-t graph 4.7 Graphs of Motion 72. Displacement-Versus-Time in free fall d-t graph a) displacement d on Y axis b) Time on X axis

4.7 Graphs of Motion 73. The d –t graph of free fall is parabolic.

4.7 Graphs of Motion 74. The relationship between distance and time is nonlinear. The relationship is quadratic and the curve is parabolic 75. when t doubled, d is quadrupled. Distance depends on time squared!

4.7 Graphs of Motion 76. The slope of the curved line is different at different points. 77. The slope on a d-t graph is velocity, the rate at which displacement is covered per unit of time. 78. The slope is steeper as time passes. This shows that speed increases with time.

4.7 Graphs of Motion What does a slope of a speed-versus-time graph represent?

4.8 Air Resistance and Falling Objects 79. Air resistance is friction experienced by object in movement wrt air

4.8 Air Resistance and Falling Objects 80. Air resistance noticeably slows the motion of objects with large surface areas like falling feathers or pieces of paper. 81. But air resistance is less noticeable on more compact objects like marbles and baseballs.

4.8 Air Resistance and Falling Objects 82. If there is no air resistance, all objects free fall at same rate.

4.8 Air Resistance and Falling Objects 83. If air resistance is small, it is negligible and we ignore it in our calculations.

4.8 Air Resistance and Falling Objects How does air resistance affect falling objects?

4.9 How Fast, How Far, How Quickly How Fast Changes Acceleration is the rate at which velocity itself changes.

4.9 How Fast, How Far, How Quickly How Fast Changes 84. Remember Don’t mix up “how fast” with “how far.” How fast is as speed: v = gt. How far is a distance: d = 1/2gt2

4.9 How Fast, How Far, How Quickly How Fast Changes 85.Acceleration is not velocity, nor is it a change in velocity Acceleration is the RATE of change of velocity.

4.9 How Fast, How Far, How Quickly How Fast Changes What is the relationship between velocity and acceleration?

Assessment Questions Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is 2 m/s. 5 m/s. 8 m/s. 12 m/s.

Assessment Questions Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is 2 m/s. 5 m/s. 8 m/s. 12 m/s. Answer: D

Assessment Questions A gazelle travels 2 km in a half hour. The gazelle’s average speed is 1/2 km/h. 1 km/h. 2 km/h. 4 km/h.

Assessment Questions A gazelle travels 2 km in a half hour. The gazelle’s average speed is 1/2 km/h. 1 km/h. 2 km/h. 4 km/h. Answer: D

Assessment Questions Constant speed in a constant direction is constant velocity. constant acceleration. instantaneous speed. average velocity.

Assessment Questions Constant speed in a constant direction is constant velocity. constant acceleration. instantaneous speed. average velocity. Answer: A

Assessment Questions A vehicle undergoes acceleration when it gains speed. decreases speed. changes direction. all of the above

Assessment Questions A vehicle undergoes acceleration when it gains speed. decreases speed. changes direction. all of the above Answer: D

Assessment Questions If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as 10 m/s/s. 10 m/s2. v = gt. both A and B.

Assessment Questions If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as 10 m/s/s. 10 m/s2. v = gt. both A and B. Answer: D

Assessment Questions A rock falls 180 m from a cliff into the ocean. How long is it in free fall? 6 s 10 s 18 s 180 s

Assessment Questions A rock falls 180 m from a cliff into the ocean. How long is it in free fall? 6 s 10 s 18 s 180 s Answer: A

Assessment Questions The slope of a speed-versus-time graph represents distance traveled. velocity. acceleration. air resistance.

Assessment Questions The slope of a speed-versus-time graph represents distance traveled. velocity. acceleration. air resistance. Answer: C

Assessment Questions In a vacuum tube, a feather is seen to fall as fast as a coin. This is because gravity doesn’t act in a vacuum. air resistance doesn’t act in a vacuum. greater air resistance acts on the coin. gravity is greater in a vacuum.

Assessment Questions In a vacuum tube, a feather is seen to fall as fast as a coin. This is because gravity doesn’t act in a vacuum. air resistance doesn’t act in a vacuum. greater air resistance acts on the coin. gravity is greater in a vacuum. Answer: B

Assessment Questions Speed and acceleration are actually one and the same concept, but expressed differently. rates of one another. entirely different concepts. expressions of distance traveled.

Assessment Questions Speed and acceleration are actually one and the same concept, but expressed differently. rates of one another. entirely different concepts. expressions of distance traveled. Answer: C

Check these calculations v = at so a = v/t a=50 m/sec = 10 m/sec2 5 sec d = ½ gt2 = 5t2 = 5(5)5 d= 125 m