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# 8.1 The language of motion PowerPoint PPT Presentation

8.1 The language of motion. 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.

8.1 The language of motion

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## 8.1 The language of motion

### 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

• 400 m

• 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

vs.

Velocity

(c) McGraw Hill Ryerson 2007

### 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

### 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

### 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

### 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 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

4

3

2

1

1

2

3

4

5

6

7

9

10

8

position (cm)

time (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.