1. Representing Motion
Chapter 2

2. Do Now Why is it important to describe and analyze motion?
What are some of the different types of motion?

3. Chapter Objectives
Represent motion through the use of words, motion diagrams, and graphs.
Use the terms position, distance, displacement, and time interval in a scientific manner to describe motion.

4. Motion Motion is instinctive Object changes position
Eyes will notice moving objects more readily than stationary ones
Object changes position
Motion can occur in many directions and paths

5. Ch 2.1 Picturing Motion Analyze motion diagrams to describe motion.
Develop a particle model to represent a moving object.

6. Picturing Motion A description of motion relates to a PLACE and TIME.
Answers the questions WHERE? and WHEN?
PLACE
TIME

7. Motion Diagram & Particle Model

8. Particle Model
Simplified version of a motion diagram in which the object in motion is replaced by a series of single points
Size of object must be much less than the distance it moves

9. Describe the motion of the bird…
Draw a particle model….

10. Describe motion of the car…
Draw a particle model…
Draw a particle model…

11. How are the two particle models different? Describe the motion of each.

12. Disregard the movements of the arms and legs
Explain how applying the particle model produces a simplified version of a motion diagram?
Disregard the movements of the arms and legs
Concentrate on a single point at the center of the body
Imagine the runner as a very small object located at the single point

13. Which statement describes best the motion diagram of an object in motion?
A. a graph of the time data on a horizontal axis and the position on a vertical axis
B. a series of images showing the positions of a moving object at equal time intervals
C. a diagram in which the object in motion is replaced by a series of single points
D. a diagram that tells us the location of the zero point of the object in motion and the direction in which the object is moving

14. What is the purpose of drawing a motion diagram or a particle model?
A. to calculate the speed of the object in motion
B. to calculate the distance covered by the object in a particular time
C. to check whether an object is in motion
D. to calculate the instantaneous velocity of the object in motion

15. Practice
Use a particle model to draw motion diagrams for two runners in a race, when the first runner crosses the finish line as the other runner is three-fourths of the way to the finish line.

16. Ch 2.2 Objectives Define coordinate systems
Recognize that the chosen coordinate system affects the sign of object’s positions
Define displacement
Determine time interval
Use a motion diagram to answer questions about an object’s position or displacement

17. Coordinate System
Tells you the location of the zero point of the variable you are studying and the direction in which the values of the variable increase.
ORIGIN
The point at which both variables have the value zero

18. Coordinate System Motion is RELATIVE
You can define a coordinate system any way you want, but some are more useful than others.
This coordinate system is set up to start (origin) at the point where the runner starts.

19. Coordinate systems
Axis of the coordinate system
This coordinate system works as well but is not as convenient to use as the first one.
Try to always pick your origin where motion begins.

20. Position & Distance
You can indicate how far an object is from the origin by drawing an arrow from the origin to the point representing the object.
The two arrows indicate the runner’s POSITION at two different times.
The length of how far an object is from the origin indicates DISTANCE.

21. Refer to the figure and calculate the distance between the two signals?
A. 3 m
B. 8 m
C. 5 m
D. 5 cm

22. Vectors & Scalars
SCALARS: quantities that are just numbers without any direction
Magnitude only
Examples: time, volume, mass
VECTORS: quantities that have both magnitude (size) and direction
Represented by arrows
Examples: velocity, acceleration, force, momentum
Tail
Tip

23. Vector Addition Just like we can add scalars, we can also add vectors.
RESULTANT: vector that represents the sum of two or more vectors.
Can add vectors algebraically or graphically

24. Vector Addition: Tail to Tip
Graphically
Place vectors tail to tip
Place the tail of the 2nd vector next to the tip of the 1st vector
The resultant is the vector drawn from the tail of the first vector to the tip of the last vector.

25. Example: Add the three vectors

26. Resultant Vector 1 Vector 2 Vector 2 Vector 1
Like scalars, vectors can be added in different order and still have the same resultant.

27. Vectors For now, we will stick to vectors that are one dimensional.
Ex: Jarred walks 75 m down the block heading east when he realizes he dropped his book. He turns around and walks 15 m until he finds his book.
Draw vectors to represent Jarred’s motion.
Find the distance that Jarred walked.
Find Jarred’s displacement.

28. Distance vs. Displacement
Actual length traveled
Scalar measurement
Path dependent
DISPLACEMENT
Change in position
Vector measurement
Path independent
∆x = xf – xi

29. Distance vs. Displacement
Find distance and displacement for the following races:
Race
Distance
Displacement
100 m
400 m
1 mile

30. Ch. 2.3 Objectives Develop position-time graphs for moving objects.
Use position-time graphs to interpret an object’s position or displacement.
Make motion diagrams, pictorial representations, and position-time graphs that are equivalent in describing an object’s motion.

31. Graphs Named as y-axis vs. x-axis Also as Dependent vs. Independent
Ex. Position vs. time
Place position on the y-axis and time on the x-axis
Always play close attention to the units.
Units are key to analyzing graphs…

32. Analyzing Graphs
When analyzing graphs always check for the following two things:
Slope: Look at the units of the slope to see if it corresponds to a measurement.
Area under the curve: look at the units for the area under the curve to see if it corresponds to a measurement.

33. Position-Time Graphs Position on y-axis Time on the x-axis
Dependent Variable
Time on the x-axis
Independent Variable
Slope = average velocity
Position-Time graphs can be used the answer the questions Where? & When?

34. From the following position-time graph of two brothers running a 100-m dash, at what time do both brothers have the same position? At what position?
At about 6 seconds
At about 60 meters

35. Position-Time Graphs When does runner B pass runner A?
45 seconds into the race
Where does runner B pass runner A?
190 m

36. Position-Time Graphs
What is the displacement of the runner between 5 s and 10 s?
10 m

37. What is happening in this graph?

38. What is happening in each?D. B.

39. Position-Time Graph Analyze the units Slope = rise over run
m = ∆y / ∆x
Slope = m / s
m/s is the unit for speed (velocity)
The slope of a position-time graph is the average velocity

40. Position-Time Graph Analyze units only Area under the curve
Area of a triangle A = ½ b * h
½ is a constant and has no units
Base has units of time (s)
Height has units of position (m)
Area = (s)(m)
We do not have any measurements that have the units (s)(m): thus the area of a position-time graph does not have any meaning.

41. Ch. 2.4 Objectives Define Velocity
Differentiate between speed and velocity
Create pictorial, physical, and mathematical models of motion problems

42. Average Velocity
Defined as the change in position, divided by the time during which the change occurred.
How fast in a given direction?
Vector quantity
Same direction as the displacement (Δx)

43. Instantaneous Velocity
Velocity at a given instant
Slope of tangent line drawn on the x-t graph at the given instant
Need calculus to find unless object moving at a constant velocity

44. Velocity vs. Speed
Speed is the distance divided by the time during which the distance was traveled.
Scalar (No direction)
Race
Distance (m)
Displacement (m)
Time (s)
Speed (m/s)
Velocity (m/s)
100 m 20
400 m 80
1 mile
400

45. Pg 37 #8
A car travels straight along the street from the grocery store to the post office. To represent its motion you use a coordinate system with its origin at the grocery store and the direction of the car is moving in the positive direction. Your friend uses the coordinate system with its origin at the post office and the opposite direction as the positive direction. Would the two of you agree on the car’s position? Distance? Displacement? Time interval? Explain!

46. Position-Time Graphs - Velocity
Suppose you recorded two joggers in one motion diagram, as shown in the figure below. From one frame to the next, you can see that the position of the jogger in red shorts changes more than that of the one wearing blue.

47. Position-Time Graphs
You can create a position-time graph if you know the position and time of the joggers at different points.
Need a minimum of two data points in order to create a x-t graph.

48. Position-Time Graphs (velocity)
Can find the velocity of each jogger by calculating the slope of the line.
Red Jogger
v = m = (6m – 2 m)/ (3s – 1s)
v = 2 m/s
Blue Jogger
v = m = (3m – 2m) / (3s – 2s)
v = 1 m/s

49. What is happening?
1 - Compare the velocities for each of the segments. Rate the segments in increasing velocity
2- Rate the segments in increasing speed.
3 – Describe the motion of the graph.

50. 5 – Step Problem Solving Method
Givens – variables, numbers, and units only
Unknown – variable, question mark, units
Formula – copy formula from formula sheet
Substitution – substitute numbers with units
Solution – box final answer, variable, number, and units