1. 8.1 The language of motion

2. 8.1 LEARNING OUTCOMES
Vector quantities, such as displacement and velocity, have both a magnitude and a direction.
An object in uniform motion will travel equal displacements in equal time intervals.
An object in uniform motion is represented as a straight line on a position-time graph.

3. TERMS TO KNOW Displacement Distance Position Position-time Graph
Scalars
Slope
Uniform Motion
Vectors
Velocity

4. 8.1 THE LANGUAGE OF MOTION Distance Time Speed Position
Many words are used when describing motion.
Many of these words have specific meanings in science.
Some common words used to describe motion include:
Distance
Time
Speed
Position

5. 8.1 THE LANGUAGE OF MOTION cont...
Describe the motion of the soccer ball before and after it is kicked.
What key words did you use when describing this situation?

6. DIRECTION MAKES A DIFFERENCE
Quantities that are measured or counted have a magnitude but may also contain a direction.
Magnitude refers to the size of a measurement or the amount you are counting.
Every time you use a map or give directions, you are using vectors.

7. DIRECTION MAKES A DIFFERENCE cont…
Quantities that describe magnitude but do not include direction are called scalar quantities or scalars.
Example: 25 seconds
Quantities that describe magnitude and also include direction are called vector quantities or vectors.
Example: 5 km north

8. DISTANCE AND POSITION
Distance (d) is a scalar quantity that describes the length of a path between two points or locations.
Example: A person ran a distance of 400 m.
Position ( ) is a vector quantity that describes a specific point relative to a reference point.
Example: The school is 3.0 km east of my house.

9. DISTANCE AND POSITION cont…
The SI unit for both distance and position is metres, m.
A car leaves home and drives 10 km to the store and then returns home. The car has driven a total distance of 20 km but its final displacement is 0 km.

10. TIME INTERVAL AND POSITION
Time (t) is a concept that describes when an event occurs.
Initial time (ti) is when the event began.
Final time (tf) is when the event finished.
Time interval is the difference between the final and initial times.

11. TIME INTERVAL AND POSITION cont…
Time interval is calculated by:
The time interval to move from the fire hydrant to the sign is calculated by:
The position of the sign is 7 m east of the tree.

12. DISPLACEMENT AND DISTANCE
Displacement describes the straight-line distance and direction from one point to another.
Displacement describes how much an object’s position has changed.
Displacement is equal to the final position minus the initial position.

13. DISPLACEMENT AND DISTANCE cont…
The SI unit for displacement is metres, m.
Between 2 s and 5 s the skateboarder’s displacement is 5 m [E]. The skateboarder’s distance travelled is 5 m.

14. WATCH FOR SIGNS
When using vector quantities, opposite directions are given opposite signs.

15. WATCH FOR SIGNS cont… Common sign conventions
Between 0 s and 15 s the person’s displacement is
= 10 m [W] – 5 m [E]
= -10 m – 5 m
= -15 m
= 15 m [W]
What distance did the person walk in this same time interval?

16. UNIFORM MOTION
Objects in uniform motion travel equal displacements in equal time intervals.
Objects in uniform motion do not speed up, slow down, or change direction.

17. UNIFORM MOTION cont…
The position of the ball in this photo is shown at equal time intervals. How would you determine if this motion is uniform motion?

18. GRAPHING UNIFORM MOTION
Motion of an object can be analyzed by drawing a position-time graph.
A position-time graph plots position data on the vertical axis (y axis) and time data on the horizontal axis (x axis).
A straight line passing through the plotted data indicates uniform motion.

19. GRAPHING UNIFORM MOTION cont…
A best-fit line is a smooth curve or straight line that most closely fits the general shape outlined by the points.
Uniform motion is represented by a straight line on a position-time graph.
The straight line passes through all the plotted points.

20. SLOPE
The slope of a graph refers to whether a line is horizontal or goes up or down at an angle.
Positive slope
Slants up to the right
Indicates motion in the direction of the positive y axis

21. SLOPE cont… Zero slope Negative slope Horizontal line
Indicates that the object is stationary
Negative slope
Slants down to the right
Indicates motion in the direction of the negative y axis
Take the Section 8.1 Quiz

22. Distance What does the word “distance” mean? -write a short definition
-the length of a path between two points
Does “distance” give any indication of direction?

23. Displacement
Describes the straight-line distance and direction from one point to another
When you run around a running track and return to where you started
your distance is ….
400 m
Your displacement is…
0 m

24. Distance is a scalar quantity… has only magnitude (size or number)…no direction
Displacement is a vector quantity….has both magnitude and direction

25. Practice
Determine the distance traveled (from A to B) and the displacement for each of the following.
A B m m B A B
400 m oval A
400 m oval

26. Position Position is a vector quantity that requires a reference point
Describe the position using 2 different reference points. W E
Home Store
O km km km

27. In Physics a reference point is often given a position of “0”.
Objects to the right are “+”
Objects to the left are “-”
-3m m m m m m

28. Dd D = “change in” Dd = df-di
final displacement – initial displacement
Determine the displacement of the car below.
-8km km

29. What is the displacement of the car? What does the “-” mean?
-8km km
What is the displacement of the car?
-18 km
What does the “-” mean?
- can mean “to the left” or “West”
Describe the position of each car with respect to a reference point.

30. Dt
Dt = tf-ti
This formula can allow us to find a time interval for a traveling object.
0 s s s s s s s s s s s s
How long did it take the motorcycle to travel ….. from the stop sign to the tree?
from the tree to the house?

31. 8.2 Average Velocity
Speed
vs.
Velocity
(c) McGraw Hill Ryerson 2007

32. 8.2 Average Velocity Speed ( ) Velocity ( ) distance / time interval.
scalar
metres per second (m/s).
Velocity ( )
displacement /time interval.
Vector; must include direction.
direction of the velocity is the same as the direction of the displacement.
These two ski gondolas have the same speed but have different velocities since they are travelling in opposite directions.
See pages
(c) McGraw Hill Ryerson 2007

33. Calculating the Slope of the Position-Time Graph
The slope of a graph is represented by rise/run.
On a position-time graph the slope is the change in position ( ) divided by the change in time ( ).
The steeper the slope the greater velocity.
Which jogger’s motion has a greater slope?
Which jogger is moving faster?
See pages
(c) McGraw Hill Ryerson 2007

34. Average Velocity
The slope of a position-time graph is the object’s average velocity.
The symbol of average velocity is:
See pages
(c) McGraw Hill Ryerson 2007

35. Calculating Average Velocity
The relationship between average velocity, displacement, and time is given by:
Use the above equation to answer the following:
What is the average velocity of a dog that takes 4.0 s to run forward 14 m?
A boat travels 280 m East in a time of 120 s. What is the boat’s average velocity?
See pages
Answers on the next slide.
(c) McGraw Hill Ryerson 2007

36. Calculating Average Velocity
The relationship between average velocity, displacement, and time is given by:
Use the above equation to answer the following:
What is the average velocity of a dog that takes 4.0 s to run forward 14 m? (3.5 m/s forward)
A boat travels 280 m East in a time of 120 s. What is the boat’s average velocity? (2.3 m/s East)
See pages
(c) McGraw Hill Ryerson 2007

37. Calculating Displacement
The relationship between displacement, average velocity, and time is given by:
Use the above equation to answer the following:
What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s?
A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s?
See page 32
Answers on the next slide.

38. Calculating Displacement
The relationship between displacement, average velocity, and time is given by:
Use the above equation to answer the following:
What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s? (120 m [N])
A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s? (78 m west)
See page 32
(c) McGraw Hill Ryerson 2007

39. Calculating Time
The relationship between time, average velocity, and displacement is given by:
Use the above equation to answer the following:
How long would it take a cat walking north at 0.80 m/s to travel 12 m north?
A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long?
See page 33
Answers on the next slide.

40. Calculating Time
The relationship between time, average velocity, and displacement is given by:
Use the above equation to answer the following:
How long would it take a cat walking north at 0.80 m/s to travel 12 m north? (15 s)
A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long? (0.73 s)
See page 33

41. Converting between m/s and km/h
To convert from km/h to m/s
Change km to m: 1 km = 1000 m
Change h to s: 1 h = 3600 s
Therefore multiply by 1000 and divide by 3600 or
Divide the speed in km/h by 3.6 to obtain the speed in m/s.
For example, convert 75 km/h to m/s.
Speed zone limits are stated in kilometres per hour (km/h).
See page 33
(c) McGraw Hill Ryerson 2007

42. Converting between m/s and km/h
Try the following unit conversion problems yourself.
Convert 95 km/h to m/s.
A truck’s displacement is 45 km north after driving for 1.3 hours. What was the truck’s average velocity in km/h and m/s?
What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval?
See next slide for answers
See page 34
(c) McGraw Hill Ryerson 2007

43. Converting between m/s and km/h
Try the following unit conversion problems yourself.
1. Convert 95 km/h to m/s. (26 m/s)
2. A truck’s displacement is 45 km north after driving for 1.3 hours. What was the truck’s average velocity in km/h and m/s?
(35 km/h [N], 9.6 m/s [N])
3. What is the displacement of an airplane flying
480 km/h [E] during a 5.0 min time interval?
(40 km [E] or 40, 000 m [E])
See page 34
Take the Section 8.2 Quiz
(c) McGraw Hill Ryerson 2007

44. Position-Time and Velocity-Time Graphs

45. Questions for Consideration
What is a position-time graph?
What is a velocity-time graph?
How do features on one graph translate into features on the other?

46. Position-Time Graphs Show an object’s position as a function of time.
x-axis: time
y-axis: position

47. Position-Time Graphs 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s
Imagine a ball rolling along a table, illuminated by a strobe light every second.
You can plot the ball’s position as a function of time.
0 s
1 s
2 s
3 s
4 s
5 s
6 s
7 s
8 s
9 s
10 s

48. Position-Time Graphs 1 2 3 4 5 6 7 8 9 10
position (cm)
time (s)

49. Position-Time Graphs What are the characteristics of this graph?
Straight line, upward slope
What kind of motion created this graph?
Constant speed 1 2 3 4 5 6 7 8 9 10
time (s)
position (cm)

50. Position-Time Graphs
Each type of motion has a characteristic shape on a P- T graph.
Constant speed
Zero speed (at rest)
Accelerating (speeding up)
Decelerating (slowing down)

51. Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
time (s)
pos. (m)
Constant speed in positive direction.
time (s)
pos. (m)
Constant speed in negative direction.

52. Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
time (s)
pos. (m)
A horizontal segment means the object is at rest.

53. Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
time (s)
pos. (m)
Speeding up in positive direction.
time (s)
pos. (m)
Speeding up in negative direction.

54. Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
time (s)
pos. (m)
Traveling in positive direction, but slowing down.
time (s)
pos. (m)
Traveling in negative direction, but slowing down.

55. Position-Time Graphs
The slope of a P-T graph is equal to the object’s velocity in that segment.
slope =
change in y
change in x
time (s)
position (m) 10 20 30 40 50
slope =
(30 m – 10 m)
(30 s – 0 s)
slope =
(20 m)
(30 s)
slope = 0.67 m/s

56. Position-Time Graphs
The following P-T graph corresponds to an object moving back and forth along a straight path. Can you describe its movement based on the graph?
time (s)
position (m) N S

57. Velocity-Time Graphs
A velocity-time (V-T) graph shows an object’s velocity as a function of time.
A horizontal line = constant velocity.
A straight sloped line = constant acceleration.
Acceleration = change in velocity over time.
Positive slope = positive acceleration.
Not necessarily speeding up!
Negative slope = negative acceleration.
Not necessarily slowing down!

58. Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity.
time (s)
velocity (m/s) N S
Object is moving at a constant velocity North.

59. Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity.
time (s)
velocity (m/s) N S
Object is moving at a constant velocity South.

60. Velocity-Time Graphs If an object isn’t moving, its velocity is zero.
time (s)
velocity (m/s) N S
Object is at rest

61. Velocity-Time Graphs
If the V-T line has a positive slope, the object is undergoing acceleration in positive direction.
If v is positive also, object is speeding up.
If v is negative, object is slowing down.

62. Velocity-Time Graphs V-T graph has positive slope. N S
time (s)
velocity (m/s) N S
Positive velocity and positive acceleration: object is speeding up!
time (s)
velocity (m/s) N S
Negative velocity and positive acceleration: object is slowing down.

63. Velocity-Time Graphs
If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction.
If v is positive, the object is slowing down.
If v is negative also, the object is speeding up.

64. Velocity-Time Graphs V-T graph has negative slope. N S
time (s)
velocity (m/s) N S
Positive velocity and negative acceleration: object is slowing down,
time (s)
velocity (m/s) N S
Negative velocity and negative acceleration: object is speeding up! (in negative direction)