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Chapter 2:
Representing Motion
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Splash Screen

2. In this chapter you will:
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.
Chapter Intro

3. Chapter 2: Representing Motion
Section 2.1: Picturing Motion
Section 2.2: Where and When?
Section 2.3: Position-Time Graphs
Section 2.4: How Fast?
Table of Contents

4. In this section you will:
Draw motion diagrams to describe motion.
Develop a particle model to represent a moving object.
Section 2.1-1

5. All Kinds of Motion
Perceiving motion is instinctive—your eyes pay more attention to moving objects than to stationary ones. Movement is all around you.
Movement travels in many directions, such as the straight-line path of a bowling ball in a lane’s gutter, the curved path of a tether ball, the spiral of a falling kite, and the swirls of water circling a drain.
Section 2.1-2

6. All Kinds of Motion
When an object is in motion, its position changes. Its position can change along the path of a straight line, a circle, an arc, or a back-and- forth vibration.
Section 2.1-3

7. Movement Along a Straight Line
A description of motion relates to place and time. You must be able to answer the questions of where and when an object is positioned to describe its motion.
Section 2.1-4

8. Movement Along a Straight Line
In the figure below, the car has moved from point A to point B in a specific time period.
Section 2.1-5

9. Click image to view movie.
Motion Diagrams
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Section 2.1-6

10. Question 1
Explain how applying the particle model produces a simplified version of a motion diagram?
Section 2.1-7

11. Answer 1
Answer: Keeping track of the motion of the runner is easier if we disregard the movements of the arms and the legs, and instead concentrate on a single point at the center of the body. In effect, we can disregard the fact that the runner has some size and imagine that the runner is a very small object located precisely at that central point. A particle model is a simplified version of a motion diagram in which the object in motion is replaced by a series of single points.
Section 2.1-8

12. Question 2
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
Section 2.1-9

13. Answer 2
Reason: A series of images showing the positions of a moving object at equal time intervals is called a motion diagram.
Section

14. Question 3
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
Section

15. Answer 3
Reason: In a motion diagram or a particle model, we relate the motion of the object with the background, which indicates that relative to the background, only the object is in motion.
Section

16. End of Section 2.1

17. In this section you will:
Define coordinate systems for motion problems.
Recognize that the chosen coordinate system affects the sign of objects’ positions.
Define displacement.
Determine a time interval.
Use a motion diagram to answer questions about an object’s position or displacement.
Section 2.2-1

18. Coordinate Systems
A 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.
The origin is the point at which both variables have the value zero.
Section 2.2-2

19. Coordinate Systems
In the example of the runner, the origin, represented by the zero end of the measuring tape, could be placed 5 m to the left of the tree.
Section 2.2-3

20. Coordinate Systems
The motion is in a straight line, thus, your measuring tape should lie along that straight line. The straight line is an axis of the coordinate system.
Section 2.2-4

21. Coordinate Systems
You can indicate how far away an object is from the origin at a particular time on the simplified motion diagram by drawing an arrow from the origin to the point representing the object, as shown in the figure.
Section 2.2-5

22. Coordinate Systems
The two arrows locate the runner’s position at two different times.
Section 2.2-6

23. Coordinate Systems
The length of how far an object is from the origin indicates its distance from the origin.
Section 2.2-7

24. Coordinate Systems
The arrow points from the origin to the location of the moving object at a particular time.
Section 2.2-8

25. Coordinate Systems
A position 9 m to the left of the tree, 5 m left of the origin, would be a negative position, as shown in the figure below.
Section 2.2-9

26. Vectors and Scalars
Quantities that have both size, also called magnitude, and direction, are called vectors, and can be represented by arrows.
Quantities that are just numbers without any direction, such as distance, time, or temperature, are called scalars.
Section

27. Vectors and Scalars
To add vectors graphically, the length of a vector should be proportional to the magnitude of the quantity being represented. So it is important to decide on the scale of your drawings.
The important thing is to choose a scale that produces a diagram of reasonable size with a vector that is about 5–10 cm long.
Section

28. Vectors and Scalars
The vector that represents the sum of the other two vectors is called the resultant.
The resultant always points from the tail of the first vector to the tip of the last vector.
Section

29. Time Intervals and Displacement
The difference between the initial and the final times is called the time interval.
Section

30. Time Intervals and Displacement
The common symbol for a time interval is ∆t, where the Greek letter delta, ∆, is used to represent a change in a quantity.
Section

31. Time Intervals and Displacement
The time interval is defined mathematically as follows:
Although i and f are used to represent the initial and final times, they can be initial and final times of any time interval you choose.
Section

32. Time Intervals and Displacement
Also of importance is how the position changes. The symbol d may be used to represent position.
In physics, a position is a vector with its tail at the origin of a coordinate system and its tip at the place where the object is located at that time.
Section

33. Time Intervals and Displacement
The figure below shows ∆d, an arrow drawn from the runner’s position at the tree to his position at the lamppost.
Section

34. Time Intervals and Displacement
The change in position during the time interval between ti and tf is called displacement.
Section

35. Time Intervals and Displacement
The length of the arrow represents the distance the runner moved, while the direction the arrow points indicates the direction of the displacement.
Displacement is mathematically defined as follows:
Displacement is equal to the final position minus the initial position.
Section

36. Time Intervals and Displacement
To subtract vectors, reverse the subtracted vector and then add the two vectors. This is because A – B = A + (–B).
The figure a below shows two vectors, A, 4 cm long pointing east, and B, 1 cm long also pointing east. Figure b shows –B, which is 1 cm long pointing west. The resultant of A and –B is 3 cm long pointing east.
Section

37. Time Intervals and Displacement
To determine the length and direction of the displacement vector, ∆d = df − di, draw −di, which is di reversed. Then draw df and copy −di with its tail at df’s tip. Add df and −di.
Section

38. Time Intervals and Displacement
To completely describe an object’s displacement, you must indicate the distance it traveled and the direction it moved. Thus, displacement, a vector, is not identical to distance, a scalar; it is distance and direction.
While the vectors drawn to represent each position change, the length and direction of the displacement vector does not.
The displacement vector is always drawn with its flat end, or tail, at the earlier position, and its point, or tip, at the later position.
Section

39. Question 1 Differentiate between scalar and vector quantities.
Section

40. Answer 1
Answer: Quantities that have both magnitude and direction are called vectors, and can be represented by arrows. Quantities that are just numbers without any direction, such as time, are called scalars.
Section

41. Question 2 What is displacement?
A. the vector drawn from the initial position to the final position of the motion in a coordinate system
B. the distance between the initial position and the final position of the motion in a coordinate system
C. the amount by which the object is displaced from the initial position
D. the amount by which the object moved from the initial position
Section

42. Answer 2
Reason: Options B, C, and D are all defining the distance of the motion and not the displacement. Displacement is a vector drawn from the starting position to the final position.
Section

43. Question 3
Refer to the adjoining figure and calculate the time taken by the car to travel from one signal to another signal?
A. 20 min
B. 45 min
C. 25 min
D. 5 min
Section

44. Answer 3 Reason: Time interval t = tf – ti
Here tf = 01:45 and ti = 01:20
Therefore, t = 25 min
Section