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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.

TERMS TO KNOW

Displacement

Distance

Position

Position-time Graph

Scalars

Slope

Uniform Motion

Vectors

Velocity

8.1 THE LANGUAGE OF MOTION

- 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

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?

DIRECTION MAKES A DIFFERENCE

Every time you use a map or give directions, you are using vectors.

- 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.

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

DISTANCE AND POSITION

- Distance (d) is a scalar quantity that describes thelength 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.

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.

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.

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.

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.

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.

WATCH FOR SIGNS

When using vector quantities, opposite directions are given opposite signs.

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?

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.

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?

GRAPHING UNIFORM MOTION

A straight line passing through the plotted data indicates 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).

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.

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

SLOPE cont…

Take the Section 8.1 Quiz

- Zero 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

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?

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

Distance is a scalar quantity… has only magnitude (size or number)…no direction

Displacement is a vectorquantity….has both magnitude and direction

Practice

Determine the distance traveled (from A to B) and the displacement for each of the following.

AB 0 m 400m

B

A

B

400 m oval

A

400 m oval

Position

Position is a vector quantity that requires a reference point

Describe the position using 2 different reference points.

E

W

Home Store

O km 2 km 10 km

In Physics a reference point is often given a position of “0”.

- Objects to the right are “+”
- Objects to the left are “-”

-3m -2m -1m 0 1m 2m 3m

Dd

- D = “change in”
- Dd = df-di

final displacement – initial displacement

Determine the displacement of the car below.

-8km -6 -4 -2 0 2 4 6 8 10 12 14 km

-8km -6 -4 -2 0 2 4 6 8 10 12 14 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.

Dt

- Dt = tf-ti
- This formula can allow us to find a time interval for a traveling object.

0 s 2s 4s 6s 8s 10s 12s 14s 16s 18s 20s 22s

How long did it take the motorcycle to travel ….. from the stop sign to the tree?

..... from the tree to the house?

8.2 Average Velocity

- Speed ( )
- 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.
- metres per second (m/s).

These two ski gondolas have the same speed but have different velocities since they are travelling in opposite directions.

See pages 26 - 27

(c) McGraw Hill Ryerson 2007

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 28 - 29

(c) McGraw Hill Ryerson 2007

Average Velocity

- The slope of a position-time graph is the object’s average velocity.
- The symbol of average velocity is:

See pages 28 - 29

(c) McGraw Hill Ryerson 2007

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 31 - 32

(c) McGraw Hill Ryerson 2007

Answers on the next slide.

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 31 - 32

(c) McGraw Hill Ryerson 2007

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.

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

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.

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

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

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

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

(c) McGraw Hill Ryerson 2007

Take the Section 8.2 Quiz

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?

Position-Time Graphs

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

Position-Time Graphs

- 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

10

9

8

7

6

5

position (cm)

4

3

2

1

time (s)

1

2

3

4

5

6

7

9

10

8

Position-Time Graphs- What are the characteristics of this graph?
- Straight line, upward slope
- What kind of motion created this graph?
- Constant speed

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)

time (s)

time (s)

pos. (m)

pos. (m)

Constant speed in positive direction.

Constant speed in negative direction.

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.

Position-Time Graphs- Constant speed is represented by a straight segment on the P-T graph.

time (s)

time (s)

pos. (m)

pos. (m)

Speeding up in positive direction.

Speeding up in negative direction.

Position-Time Graphs- Curved segments on the P-T graph mean the object’s speed is changing.

time (s)

time (s)

pos. (m)

pos. (m)

Traveling in positive direction, but slowing down.

Traveling in negative direction, but slowing down.

Position-Time Graphs- Curved segments on the P-T graph mean the object’s speed is changing.

50

change in y

slope =

40

change in x

30

position (m)

(30 m – 10 m)

20

slope =

(30 s – 0 s)

10

(20 m)

10

20

30

40

slope =

(30 s)

time (s)

Position-Time Graphs- The slope of a P-T graph is equal to the object’s velocity in that segment.

slope = 0.67 m/s

N

position (m)

time (s)

S

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?

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!

N

velocity (m/s)

time (s)

S

Velocity-Time Graphs- A horizontal line on the V-T graph means constant velocity.

Object is moving at a constant velocity North.

N

velocity (m/s)

time (s)

S

Velocity-Time Graphs- A horizontal line on the V-T graph means constant velocity.

Object is moving at a constant velocity South.

N

velocity (m/s)

time (s)

S

Velocity-Time Graphs- If an object isn’t moving, its velocity is zero.

Object is at rest

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.

N

N

velocity (m/s)

velocity (m/s)

time (s)

time (s)

Negative velocity and positive acceleration: object is slowing down.

Positive velocity and positive acceleration: object is speeding up!

S

S

Velocity-Time Graphs- V-T graph has positive slope.

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.

N

N

velocity (m/s)

velocity (m/s)

time (s)

time (s)

Negative velocity and negative acceleration: object is speeding up! (in negative direction)

Positive velocity and negative acceleration: object is slowing down,

S

S

Velocity-Time Graphs- V-T graph has negative slope.

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