1. Unit 2: Motion

2. Penn and Teller Video

3. Frames of Reference and Reference Points
In order to understand how things move, you have to understand three basic ideas about what it means when something is moving.
Position or displacement which tells us exactly where the object is;
Speed or velocity which tells us how fast the object’s position is changing (how fast the object is moving); and
Acceleration which tells us how fast the object’s velocity is changing.

4. The word position describes your location
The word position describes your location. To just say I am here is meaningless; you must specify your position relative to a known reference point.
Example: If you are 2 meters from the doorway, inside your classroom, then your reference point is the doorway.
Notice that you need both a reference point and a direction to accurately define your location.

5. Frame of Reference: a reference point combined with a set of directions.
Example: a boy is standing still inside a train as it pulls out of the station. You are standing on the platform watching the train move from left to right. To you it looks like the boy is moving from left to right, because relative to where you are standing (the platform), he is moving. According to the boy, and his frame of reference (the train), he is not moving.

6. A frame of reference must have an origin (where you are standing on the platform) and at least a positive direction. With the train moving left to right, your right is positive and your left is negative – much like a number line.
If someone else was looking at the boy, his frame of reference will be different. If he is standing on the other side of the platform, the boy would be moving from right to left.

7. Illustration of Frame of Reference and Point of Origin
A boy inside a train which is moving from left to right.
Negative Direction
Positive Direction
Where you are standing on the platform.
(reference or point of origin)

8. Position
Position: a measurement of a location, with reference to an origin.
Positions can be positive or negative depending on the origin. The symbol x is used to indicate position. x has units of length (cm, m, km) depending on what we are measuring.
Position is a vector quantity.

9. School
Jack
John
Joan
Jill
Joel
Shop
100 m
100 m
100 m
100 m
100 m
100 m
Depending on what reference point we choose, we can say that the school is 300 meters from Joan’s house (with Joan’s house as the point of origin) or 500 meters from Joel’s house (with Joel’s house as the point of origin).

10. The shop is also 300 meters from Joan’s house, but in the opposite direction as the school. When we choose a reference point, we have a positive direction and a negative direction. If we choose the directions towards the school as positive, then the direction towards the shop is negative.
School
Joan
Shop
X (m)
+300
+200
+100
-100
-200
-300
The origin is at Joan’s house and the position of the school is +300 meters.

11. Practice Write down the positions for A,B,D, and E.
2) Write down the positions for F,G, H, and J.
A B D E
F G H J

12. You live in house C. What is your position relative to house E?
There are five houses on Newton Street, A,B,C,D, and E. For all cases, assume that positions to the right are positive.
Draw a frame of reference with house A as the origin and write down the positions of houses B,C,D, and E.
You live in house C. What is your position relative to house E?
What are the positions of houses A, B, and D, if house B is taken as the reference point? A B C D E
20 m m m m

13. Relative Motion
Relative motion is just a way of saying that sometimes different people will say different things about the motion of the same object.
This is not because one of them is wrong, but because they are using different __________.
Frames of reference

14. Examples
Let’s say I am standing on the back of a pickup truck (that is motionless), and I am throwing apples forwards. I know that I can throw an apple at exactly 15 m/s every time.
If a person were standing on the sidewalk, how fast would she say the apples are moving?
Since she will see them exactly the same way as me (we’re both in the same reference frame), she will say 15 m/s.
Now the truck starts to move forwards at 20 m/s. I am still throwing apples forwards, exactly the same as I was throwing them before, at 15 m/s.

15. If I am really not paying attention to what’s going on around me (like the fact that I am standing in the back of a moving truck), how fast would I say the apples are moving?
Still 15 m/s! Relative to me, I can only make an apple move away from me at 15 m/s, so that is how fast I measure the apple moving away from me.
How fast does my friend on the sidewalk say the apple is moving?
Well, even before I throw it, she’ll say that the apple is moving at 20 m/s (the speed of everything on the truck).

16. When I have thrown the apple forward, adding more velocity to it, she will say it is going at (20 m/s + 15 m/s) 35 m/s!
Now I turn around and start throwing the apples from the rear of the truck, backwards!
I will still say that my apples are moving at 15 m/s, because from my way of looking at it, that’s how fast the apple is moving. The only thing I might say that is different is that it is -15 m/s since even I should be able to notice they are going in the opposite direction now.
My friend on the sidewalk will say the apple is moving ___________.
5 m/s (20 m/s – 15 m/s)

17. Sitting at your desk, how fast are you moving?
Relative to the ground:
zero
Relative to the sun:
2.97 x 104 m/s
You might have even noticed relative velocity while sitting at a red light…
Have you ever been sitting at a red light with a bus stopped next to you?
You’re kind of daydreaming, looking out the window at the side of the bus, when all of a sudden it feels like your car is rolling backwards!
Then you realize that it was just the bus moving forwards.
Your brain knows that the bus was just sitting there on the road...it became part of the frame of reference of the ground.
When your brain saw the bus moving forwards, it had already “decided” that the bus won’t move. The only option remaining is that you must be moving backwards.

18. Interesting Fact
Frames of references and relative motion are actually the reason that people get car sick. Your brain is getting two different sets of information about your body’s motion that might not exactly agree with each other; information from your eyes, and information from your inner ear. Some people are more sensitive to these differences, which causes them to feel car sick as they watch the road “whiz” by. If you are prone to getting car sickness, try to look forward at a point far in the distance and stay focused on that.

19. Frame of Reference Review Worksheet

20. Motion Car Lab or Bubble Tube Lab

21. Speed vs. Velocity Speed Velocity
The ratio of the distance an object moves to the amount of time the object moves.
SI Unit: meters per second (m/s)
A scalar quantity since it does not describe direction.
The ratio of the distance an object moves to the amount of time the object moves plus the direction in which it moves.
SI Unit: meters per second (m/s) + direction
A vector quantity since it does describe direction.

22. Instantaneous Speed/Velocity: the speed at any given instant in time.
Average Speed: the average of all instantaneous speeds; found simply by a distance/time ratio.
Constant Speed/Velocity: a non-changing rate of distance over time.
An object with constant speed/velocity would cover the same distance every second.
An object with changing speed/velocity would be moving a different distance every second.

23. Calculating Speed and Velocity
The average speed during the course of a motion is often computed using the following formulas:
Average Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑟𝑎𝑣𝑒𝑙𝑒𝑑 𝑇𝑖𝑚𝑒 𝑜𝑓 𝑇𝑟𝑎𝑣𝑒𝑙
In contrast, the average velocity is often computed using this formula:
Average Velocity = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 (∆ 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛) 𝑇𝑖𝑚𝑒

24. While on vacation, Lisa traveled a total distance of 440 miles
While on vacation, Lisa traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?
s = 𝑑 𝑡 = 440 𝑚𝑖 8 ℎ𝑟 = 55 mi/hr
Lisa averaged a speed of 55 miles per hour. She may not have been traveling at a constant speed of 55 mi/hr. She undoubtedly, was stopped at some instant in time (perhaps for a bathroom break or for lunch) and she probably was going 65 mi/hr at other instants in time. Yet, she averaged a speed of 55 miles per hour.

25. Lets consider the motion of that physics teacher again.
2m m
Determine the average speed and the average velocity.

26. The physics teacher walked a distance of 12 meters in 24 seconds and ended up back where she started.
s = 𝑑 𝑡 = 12 𝑚 24 𝑠 = 0.5 m/s
v = ∆𝑥 𝑡 = 0 𝑚 24 𝑠 = 0 m/s
Remember that displacement is a change in position and velocity is based upon this position change.

27. Practice
Find the average speed and average velocity of the following: (drawing a picture might help)
A) Cross-Country Skier:
In the first minute, the skier travels 180 meters East.
In the second minute, the skier travels 140 meters West.
In the third minute, the skier travels 100 meters East.
B) Football Coach (pacing the sidelines):
In the first three minutes of the game, the coach paces 35 yards West.
In the next three minutes, the coach paces 20 yards East.
In the next four minutes, the coach paces 40 yards West.

28. Answers s = 420 𝑚 3 𝑚𝑖𝑛 = 140 m/min v = 140 𝑚 3 𝑚𝑖𝑛 = 46.7 m/min East
s = 95 𝑦𝑑 10 𝑚𝑖𝑛 = 9.5 yd/min
v = 55 𝑦𝑑 10 𝑚𝑖𝑛 = 5.5 yd/min left

29. Acceleration The rate at which an object changes its velocity.
Acceleration is a vector quantity since it describes velocity (which is also vector).
Sports announcers will occasionally say that a person is accelerating if he/she is moving fast. Acceleration has nothing to do with going fast. A person can be moving very fast and still not be accelerating.
Acceleration has to do with changing how fast an object is moving.

30. If an object is not changing its velocity, then the object is not accelerating.
If the velocity changes by a constant amount, then the acceleration is constant.
SI Unit: meters/second/second (m/s/s) OR
meters/second2 (m/s2)
An object with constant acceleration should not be confused with an object with a constant velocity. If an object is changing velocity – whether by a constant or varying amount – it is still accelerating.

31. Calculating Average Acceleration
The average acceleration (a) of any object over a given interval of time (t) can be calculated using the following equation:
Average Acceleration = ∆ 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒
∆Velocity = Vf – Vi

32. Calculate: One type of ride falls straight down for 3 seconds
Calculate: One type of ride falls straight down for 3 seconds. During this time, the ride accelerates from a speed of 0 m/s to a speed of 30 m/s. What is the average acceleration of the ride?
(30 m/s – 0 m/s)/3 sec
10 m/s2
Calculate: A roller coaster accelerates from a speed of 4 m/s to 22 m/s in 3 seconds. What is the average acceleration of the ride?
(22 m/s – 4 m/s)/3 sec
6 m/s2

33. Practice
A runner accelerates from a velocity of 5 mi/hr east until reaching a velocity of 10 mi/hr east in 20 seconds. What was the runner’s acceleration?
A car traveling at 45 km/hr south passes another car accelerating to 60 km/hr south in 5 seconds. What was the car’s acceleration?
At point A, a runner is jogging at 3 m/s. Forty seconds later, at point B, the jogger’s velocity is only 1 m/s. What is the jogger’s acceleration from point A to point B?

34. a = - 0.05 m/s/s (any direction)
Answers
a = 0.25 mi/hr/s east
a = 3 km/hr/s south
a = m/s/s (any direction)

35. More Practice
You took a car trip with your family to visit relatives who live 750 km away. The trip took 8 h. What was your average speed?
If you travel 50 km due east in 2 h, what is your velocity?
A train takes 10 min to slow down to 10 m/s from 40 m/s. What is its acceleration?

36. Answers
93.75 km/h
25 km/h due East
- 3 m/s/min

37. Calculations Review
Calculate the speed for a car that went a distance of 125 miles in 2 hours.
How much time does it take for a bird flying at a speed of 45 mi/hr to travel a distance of 1800 miles?
A baseball travels at a speed of 120 ft/sec. How far will the baseball travel in 0.5 seconds?

38. Answers
62.5 mi/hr
40 hr
60 ft

39. Math Practice 1 Worksheet Math Practice 2 Worksheet Formative Assessment 1

40. Since acceleration is a vector quantity, it has a direction associated with it. The direction of the acceleration vector depends on two things:
Whether the object is speeding up or slowing down.
Whether the object is moving in the + or – direction.
If an object is slowing down, then its acceleration is in the opposite direction of its motion.

41. Consider the two data tables above
Consider the two data tables above. In each case, the acceleration of the object is in the positive direction. In Example A, the object is moving in the positive direction (has a positive velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity thus having a positive acceleration.
In Example B, the object is moving in the negative direction (has a negative velocity) and is slowing down. According to our principle, when an object is slowing down, the acceleration is in the opposite direction as the velocity; thus, this object also has a positive acceleration.

42. In Example C, the object is moving in the positive direction (has a positive velocity) and is slowing down. When an object is slowing down, the acceleration is in the opposite direction; thus the acceleration is negative.
In Example D, the object is moving in the negative direction (has a negative velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity; thus the acceleration is negative.

43. Observe the use of positive and negative as used in the discussion above (Examples A - D). In physics, the use of positive and negative always has a physical meaning. It is more than a mere mathematical symbol. As used here to describe the velocity and the acceleration of a moving object, positive and negative describe a direction. Both velocity and acceleration are vector quantities and a full description of the quantity demands the use of a directional adjective. Physics often borrows from mathematics and uses the + and - symbols as directional adjectives. Consistent with the mathematical convention used on number lines and graphs, positive often means to the right or up and negative often means to the left or down. So to say that an object has a negative acceleration as in Examples C and D is to simply say that its acceleration is to the left or down (or in whatever direction has been defined as negative). Negative accelerations do not refer acceleration values that are less than 0. An acceleration of -2 m/s/s is an acceleration with a magnitude of 2 m/s/s that is directed in the negative direction.

44. To test your understanding of the concept of acceleration, consider the following problems and the corresponding solutions. Use the equation for acceleration to determine the acceleration for the following two motions.

45. Constant Velocity Graph:
Position-Time Graphs
Constant Velocity Graph:
Consider a car moving with constant, rightward velocity. If the position-time data for such a car was graphed, the result would look like the following:
The slope of the line would be in a constant, positive direction.

46. Consider a car moving with constant, leftward velocity
Consider a car moving with constant, leftward velocity. If the position-time data for such a car was graphed, the result would look like the following:
The slope of the line would be in a constant, negative direction.

47. Changing Velocity Graph:
Consider a car moving with a rightward, changing velocity. This car would be described as “speeding up.” If the position-time data for such a car was graphed, the result would look like the following:
The slope of the line would be in a changing, positive direction.

48. Consider a car moving with changing, leftward velocity
Consider a car moving with changing, leftward velocity. If the position-time data for such a car was graphed, the result would look like the following:
The slope of the line would be in a changing, negative direction.

49. Comparing Graphs Slow, Leftward Fast, Leftward Constant Velocity
Slow, Rightward
Constant Velocity
Fast, Rightward
Constant Velocity
Negative Velocity
Slow to Fast
Negative Velocity
Fast to Slow

50. What’s Happening here?
For the first five seconds, the car is moving at constant velocity. At five seconds, the car stops and remains at rest for another 5 seconds.

51. Worksheet Packet Review and Reinforce: Speed and Velocity Enrich: Speed and Velocity Enrich: Acceleration

52. Velocity-Time Graphs
Consider a car moving with a constant, rightward (+) velocity. Since the car is moving with a constant velocity, its acceleration is zero.
The resulting graph would look like:
Note that a motion described as a constant, positive velocity results in a zero slope. Furthermore, only positive velocity values are plotted, corresponding to a motion with positive velocity.

53. Consider a car moving with a rightward (+), changing velocity – that is, a car moving in a positive direction but speeding up (accelerating).
Since the car has a positive velocity and is speeding up, the acceleration is also positive.
The resulting graph would look like:

54. How can you tell if an object is moving in a positive or negative direction?
The velocity is positive when the line lies in the positive region (above the x-axis) of the graph.
The velocity is negative when the line lies in the negative region (below the x-axis) of the graph.
If a line crosses over the x-axis, then the object has changed directions.

55. How can you tell if an object is speeding up or slowing down?
Positive and negative acceleration values do not indicate speeding up or slowing down. One must look at the magnitude or number, not the sign.
On a graph, if the line is moving away from the 0-velocity point (further from the x-axis), then the object is speeding up.
If the line is approaching the 0-velocity point, then the object is slowing down.

56. Check Your Understanding
Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true):
moving in the positive direction.
moving with a constant velocity.
moving with a negative velocity.
slowing down.
changing directions.
speeding up.
moving with a positive acceleration.
moving with a constant acceleration.

57. Answers
a: TRUE since the line is in the positive region of the graph. b. FALSE since there is an acceleration (i.e., a changing velocity). c. FALSE since a negative velocity would be a line in the negative region (i.e., below the horizontal axis). d. TRUE since the line is approaching the 0-velocity level (the x-axis). e. FALSE since the line never crosses the axis. f. FALSE since the line is not moving away from x-axis. g. FALSE since the line has a negative or downward slope. h. TRUE since the line is straight (i.e, has a constant slope).

58. Interpreting a Velocity Time Graph

59. Worksheet 1 Worksheet 3

60. Acceleration-Time Graphs Kinematic Curves

61. Kinematic Curves Practice Worksheet 1 Kinematic Curves Practice Worksheet 2

62. Free Fall Concepts
An object in free fall experiences an acceleration of -9.8 m/s/s (the – indicates downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object.
If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s/s.
If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s.
If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of 30 m/s will have a downward velocity of -30 m/s when it returns to the same height.

63. Calculating Free Fall
Free fall can be calculated using the following formula: ∆x = 1 2 at2 Where ∆x is the change in position, a is the acceleration of gravity and t is time (which is squared)

64. Free Fall Practice Worksheet

65. Free Fall Worksheet Answers
T = 1.32 seconds
D = meters
T = 1.29 seconds
D = 48 meters
D = meters

66. Formative Assessment 2 Uniform Acceleration Mock Lab