1. PHYSICS ESSENTIALS
UNIT 2:
MOTION

2. NOTE: In these notes: Vocab Log words are in RED.
Words to fill-in in your notes are UNDERLINED.
Some words may be both
UNDERLINED and in RED.

3. Motion, Distance, Displacement
Q: What is motion?
A: Motion is any change in the position of an object. Kinematics is the study of motion (without considering the cause of the motion).

4. Motion, Distance, Displacement
Distance vs. Displacement
Distance
Distance is the length an object travels along a path between two points.
Metric unit for distance = meter (m)

5. Motion, Distance, Displacement
Consists of two parts
How far the object is from its starting point
The direction the object traveled

6. Motion, Distance, Displacement
Displacement is often used when giving directions
Compare these two directions: walk 5 blocks vs. walk 5 blocks north. Which directions give you a better of idea of where to go?

7. Motion, Distance, Displacement
Practice Problem #1:
Think about the motion of a roller coaster car...
If you measure the path along which the car has traveled, you have measured the ___________.
If you consider the direction from the starting point to the car and how far the car is from where it started, you have measured the ________________.
What is the car’s displacement after one complete trip around the track? ____

8. Motion, Distance, Displacement
Displacement is an example of a vector
A vector is a quantity that has magnitude and direction
The magnitude can be size, length, or amount
We represent vectors on a graph or map with arrows
The length of the arrow is equal to the magnitude of the vector

9. Motion, Distance, Displacement
You can add displacements using
vector addition (combining vector magnitudes and directions)

10. Motion, Distance, Displacement
For displacement along a straight line
Two displacements represented by two vectors in the same direction can be added to one another (Figure A)

11. Motion, Distance, Displacement
For two displacements in opposite directions, the magnitudes subtract from one another (Figure B)

12. Motion, Distance, Displacement
For displacements that aren’t along a straight path
For two or more displacement vectors in different directions, you can combine by graphing

13. Motion, Distance, Displacement
The picture shows yellow vectors representing a boy’s path walking from home to school. The total distance walked is 7 blocks.
The vector in red represents the boy’s total displacement. Measuring this vector gives a displacement of about 5 blocks.

14. Speed Q: How can we tell how fast an object is moving?
A: By calculating its speed.

15. Speed
Speed is the distance an object travels in a certain period of time
Metric unit for speed = meters/second (m/s) or kilometers/hour (km/hr)

16. Speed We can look at speed in two ways: 1) Instantaneous Speed
How fast an object is moving at any given moment in time
Speed measured at a particular instant

17. Speed Ex: A speedometer in a car tells us instantaneous speed
Ex: A radar gun used by the police to determine whether or not you are speeding while driving

18. Speed
2) Average Speed
Average speed for the entire duration of a trip

19. Speed
Average Speed = Total Distance
Total Time
OR s = d/t d
s t

20. Speed SPEED EXAMPLE PROBLEM:
John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?

21. Step 1: What information are you given?
Speed #1= 50 miles/hr Speed #2= 60 miles/hr
Time #1= 3hours Time#2 = 2 hours
Step 2: What unknown are you trying to calculate?
Average speed
Step 3: What formula contains the given quantities and the unknowns?
Average speed = total distance
total time
Step 4: Replace each variable with its known value and solve.
50 mile x 3hrs = 150 miles 60 mile x 2hrs = 120 miles
Hour hour
Total time= 3 hours + 2 hours
Average speed = 270 miles = 54 miles/hour
5 hours

22. Speed Practice Problem #2:
While traveling on vacation, you measure the times and distances traveled. You travel 35 km in 0.4 hours, followed by 53 km in 0.6 hours. What is your average speed?

23. Step 1: What information are you given?
Distance #1 = 35 km Distance #2 =53 km
Time #1 = .4 hours Time #2 = .6 hours

24. Step 2: What unknown are you trying to calculate?
Average speed

25. Step 3: What formula contains the given quantities and the unknowns?
Average speed = Total Distance
Total time

26. Step 4: Replace each variable with its known value and solve.
Average speed = 35km + 53 km = 88km
.4 hr + .6 hr = 1hr
88km = 88km/hr
1hr

27. Step 5: Does your answer seem reasonable?
Could a car travel 88 km per hour?
Sure, that’s about 55 miles/hr

28. Speed Practice Problem #3:
It takes you 45 s to walk 72 m down the block to your friend’s house. What is your average speed?

29. Given: distance=72 m time = 45 s
Average speed = total distance
total time
Average speed = 72m = 1.6 m/s
45 s

30. Graphing Speed
Q: How can we visually represent the speed of an object?
A: A good way to describe speed is with a distance-time graph.

31. Graphing Speed Graphing Constant Speed
Constant Speed: When an object’s speed doesn’t change
Ex: A race car with a constant speed of 96 m/s travels 96 meters every second

32. Graphing Speed
Graph of constant speed is a straight, diagonal line

33. Graphing Speed
When the motion of an object is graphed by plotting the distance it travels versus time, the slope of the resulting line is the object’s speed

34. Graphing Speed Slope = (y2-y1) (x2-x1)
Choose two points on the line and plug the
coordinates into the formula

35. Graphing Speed
Practice Problem #4: draw your guess for an object moving at a slow, constant speed.

36. #4
Draw the actual Graph for slow constant speed here!!

37. #4 Pick two points and calculate slope!! Slope = Y2 – Y1 X2 – X 1
The slope will tell you the speed!!!

38. Graphing Speed
Practice Problem #5: draw your guess for an object moving at a fast, constant speed.

39. #5
Draw the actual Graph for fast constant speed here!!

40. #5 Pick two points and calculate slope!! Slope = Y2 – Y1 X2 – X 1
The slope will tell you the speed!!!

41. Graphing Speed Graphing Varying Speed
Varying Speed: When an object travels at different speeds during different parts of a trip
Ex: A car travels 10 m/s for 60 s then travels 20 m/s for the next 120 s

42. Graphing Speed
Slopes of the different parts of the trip can be calculated individually using the formula above
Slope = (y2-y1)
(x2-x1)

43. Varying Speed Graph

44. Segment #1 points (0,1) and (2,1.5)
Find slope of each segment!

45. Segment # = 1 = m/s
Segment # = 0 = 0m/s
Segment # = = -.75 m/s
Segment # = 2 = .5 m/s

46. Graphing Speed
Practice Problem #6: draw your guess for an object moving slowly for 4 sec, stopping for two seconds and then moving fast for 4 sec!

47. #6
draw the actual graph for an object moving slowly at first, stopping for two seconds and then moving fast!

48. Graphing Speed Practice Problem #7:
Answer the following questions about the graph to the right:
1) Which of the objects are moving at a constant speed?
2) Which object is traveling the fastest? How do you know?
3) Which object is traveling the slowest? How do you know?

49. All are moving at constant because they are straight lines.
Cruising jet; steepesthighest slope which is the biggest number
Walking person; slope closet to horizontal smallest number

50. Velocity
Velocity is the speed AND direction in which an object is moving
Velocity gives a more complete description of motion than speed alone

51. Velocity You solve for velocity the same way you solve for speed
Speed = distance Velocity = distance & direction
time time
Ex: 25 km/hr Ex: 25 km/hr west

52. Velocity The direction of motion can be described in various ways:
North, south, east, west
Uphill, downhill
Positive vs. negative

53. Velocity VELOCITY EXAMPLE PROBLEM:
What is the velocity of a rocket that travels 9000 meters away from the Earth in seconds?

54. Velocity Step 1: What information are you given?
Distance and Direction= 9000m away from Earth
Time= 12.12s
Step 2: What unknown are you trying to calculate?
Velocity
Step 3: What formula contains the given quantities and the unknowns?
v=distance
time
Step 4: Replace each variable with its known value and solve.
v= m = m away from Earth
12.12 s s
Step 5: Does your answer seem reasonable? yes

55. Velocity Practice Problem #8:
Find the velocity of a swimmer who swims exactly km toward the shore in 0.02 hr.

56. Step 1: What information are you given?
Distance and Direction= .110 km toward
shore
Time= .02 hr

57. Step 2: What unknown are you trying to calculate?
Velocity

58. Step 3: What formula contains the given quantities and the unknowns?
Velocity = distance and direction
time
V= d/t

59. Step 4: Replace each variable with its known value and solve.
Velocity =.110 km = 5.5km/hr toward
.02 hr shore

60. Step 5: Does your answer seem reasonable?
Yes, that’s about 8.9 miles per hour.

61. Velocity Practice Problem #9:
Find the velocity of a baseball thrown 38 m from third base toward home plate in 1.7 s.

62. V=d/t
V= 38m =22.4 m/s towards home
1.7s

63. Acceleration
Q: How can we determine if there has been a change in the velocity of an object?
A: By calculating the object’s acceleration.

64. Acceleration Acceleration is a change in velocity.
Since velocity includes both speed and direction, acceleration occurs if there is a change in speed, a change in direction, or a change in both

65. Acceleration
- Metric Unit = m/s2

66. Acceleration
Ex: A dog chases its tail – direction is changing so the dog is accelerating
Ex: A car slows down when it sees a red light – speed is changing so the car is accelerating

67. Acceleration
Ex: A car sets its cruise control and continues to head east – the speed and direction stay the same, so the car is NOT accelerating
Ex: You drop a ball off the roof of a tall building and it speeds up as it falls – speed is changing at a rate of 9.8 m/s2, so the ball is accelerating

68. Acceleration
- Society often uses the term acceleration to describe situations in which the speed of an object is increasing.

69. Acceleration
- Scientifically, however, the change may be an increase OR a decrease in speed
Acceleration is ANY change in an object’s velocity
Positive acceleration = speeding up
Negative acceleration (deceleration) = slowing down

70. Acceleration

71. Acceleration
In addition, an object can accelerate even if the speed remains constant
Ex: Riding a bike around a curve
- Although the speed remains constant, the change in direction means that you are accelerating

72. Acceleration This is known as uniform circular motion
Ex: You can also think of a carousel
The speed of the carousel remains constant throughout the ride, but the carousel is constantly changing direction
This means the carousel is accelerating

73. Acceleration

74. Acceleration
Constant Acceleration: A steady change in velocity of an object moving in a straight line
Velocity changes by the same amount each second

75. Acceleration Calculating Acceleration
Acceleration = a = Change in velocity = (v final – v initial)
Total time t

76. Acceleration ACCELERATION EXAMPLE PROBLEM:
A dragster in a race accelerated from stop to
60 m/s by the time it reached the finish line. The dragster moved in a straight line and traveled from the starting line to the finish line in 8.0 s.  What was the acceleration of the dragster?

77. Acceleration Step 1: What information are you given?
Velocity final= 60 m/s
Velocity initial 0m/s
Time = 8.0s

78. Acceleration Step 2: What unknown are you trying to calculate?

79. Acceleration
Step 3: What formula contains the given quantities and the unknowns?
Acceleration = velocity final- velocity initial
time

80. Acceleration
Step 4: Replace each variable with its known value and solve.
Acceleration= 60 m/s – 0 m/s = 60m/s=7.5
8.0s s
Acceleration = 7.5m/s2

81. Acceleration
Step 5: Does your answer seem reasonable?
Sure

82. Acceleration Practice Problem #10:
A ball rolls down a ramp starting from rest. After 2 seconds, its velocity is 6 m/s. What is the acceleration of the ball?

83. Step 1: What information are you given?
Velocity final= 6m/s Velocity initial= 0m/s
Time= 2 seconds

84. Step 2: What unknown are you trying to calculate?
acceleration

85. Step 3: What formula contains the given quantities and the unknowns?
Acceleration = velocity final- velocity initial time

86. Step 4: Replace each variable with its known value and solve.
Acceleration= 6m/s- 0ms= 3m/s2 2s

87. Acceleration Practice Problem #11:
A flower pot falls off a second story windowsill. The flower pot starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the flower pot.

88. Acceleration= 14.7 ms- 0m/s = 9.8 m/s2

89. Graphing Acceleration
You can use a speed-time graph to display and calculate acceleration
The slope of a speed-time graph
is equal to acceleration
Speed-time graphs are linear
graphs

90. Graphing Acceleration
This graph shows positive acceleration
An airplane taking off from the runway increased its speed at a constant rate because it was moving up into the sky with constant acceleration

91. Graphing Acceleration
This graph shows negative acceleration
Constant negative acceleration decreases speed
Imagine a bicycle slowing to a stop
The horizontal line segment represents constant speed
The line segment sloping downward represents the bicycle slowing down
In this case, the change in speed is negative, so the slope of the line is negative

93. Motion Diagrams
Another way to represent acceleration and velocity is through a motion diagram.
A ticker tape analysis is one way to do this.
Marks are placed on a long tape at regular intervals of time.

94. Motion Diagrams The trail of dots gives a history of an
object’s motion.

95. Motion Diagrams
The distance between the dots represents the object’s position change during that time interval.
A large distance means the object was moving fast.
A small distance means the object was moving slow.

96. Motion Diagrams

97. Motion Diagrams
Based on the dots on a ticker tape, we can also see if an object was moving with constant speed or accelerating.

98. Motion Diagrams
A constant distance between dots represents constant velocity, or no acceleration.
A changing distance between dots indicates changing velocity, also known as acceleration.

99. Motion Diagrams

100. Motion Diagrams
We can also use “Strobe Pictures” in order to show velocity and acceleration in the same way.
A camera takes a picture of an object in motion at regular intervals.

101. Motion Diagrams

102. Motion Diagrams

103. Motion Diagrams
Vector diagrams can be used to show direction and magnitude with a vector arrow.

104. Motion Diagrams
In a vector diagram, the size of the vector arrow tells us the magnitude .
If all of the arrows are the same length, then the magnitude is constant.
In the case of a moving car, this would mean that the velocity of the car is constant while it is moving.

105. Motion Diagrams
If the size of the arrows increase or decrease, this would mean that the car is changing velocity or accelerating.