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

DisplacementDistancePositionPosition-time GraphScalarsSlope Uniform MotionVectorsVelocity

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:DistanceTime SpeedPosition

Describe the motion of the soccer ball before and after it is kicked.What key words did you use when describing this situation?

8.1 THE LANGUAGE OF MOTION cont...

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.

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.

d

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:

if ttt

ssst 325

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.

d =

d f -

d i

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.

d =

d f -

d i

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?

d =

d f -

d i

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

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.

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 slopeSlants up to the rightIndicates motion in the

direction of the positive y axis

SLOPE cont…

Zero slopeHorizontal lineIndicates that the object is

stationary

Negative slopeSlants down to the rightIndicates motion in the direction of

the negative y axis

Take the Section 8.1 Quiz

DistanceWhat does the word “distance” mean?

-write a short definition

-the length of a path between two points

Does “distance” give any indication of direction?

DisplacementDescribes the straight-line distance and

direction from one point to another

When you run around a running track and return to where you startedyour distance is ….

400 mYour displacement is…

0 m

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

Displacement is a vector quantity….has both magnitude and direction

PracticeDetermine the distance traveled (from A to B) and the

displacement for each of the following.

A B

0 m 400 m

A B 400 m oval

A 400 m oval

B

Position

Position is a vector quantity that requires a reference point

Describe the position using 2 different reference points.

Home Store

O km 2 km 10 km

EW

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

DdD = “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

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.

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

DtDt = 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

(c) McGraw Hill Ryerson 2007

8.2 Average Velocity

Speed ( )distance / time interval.scalarmetres 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). See pages 26 - 27

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

v

v

v

(c) McGraw Hill Ryerson 2007

Calculating the Slope of the Position-Time GraphThe 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.

See pages 28 - 29

t

Which jogger’s motion has a greater slope?Which jogger is moving faster?

slope

d

t

d

(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

v av

(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:1. What is the average velocity of a dog that

takes 4.0 s to run forward 14 m?

2. A boat travels 280 m East in a time of 120 s. What is the boat’s average velocity?

See pages 31 - 32Answers on the next slide.

v av

d

t

(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:1. What is the average velocity of a dog that

takes 4.0 s to run forward 14 m? (3.5 m/s forward)

2. 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

v av

d

t

Calculating Displacement

The relationship between displacement, average velocity, and time is given by:

Use the above equation to answer the following:1. What is the displacement of a bicycle that

travels 8.0 m/s [N] for 15 s?

2. 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 32Answers on the next slide.

d

v av t

(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:1. What is the displacement of a bicycle that

travels 8.0 m/s [N] for 15 s? (120 m [N])

2. 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

d

v av t

Calculating Time

The relationship between time, average velocity, and displacement is given by:

Use the above equation to answer the following:1. How long would it take a cat walking north at 0.80

m/s to travel 12 m north?

2. 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 33Answers on the next slide.

t d

v av

Calculating Time

The relationship between time, average velocity, and displacement is given by:

Use the above equation to answer the following:1. How long would it take a cat walking north at 0.80

m/s to travel 12 m north? (15 s)

2. 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

t d

v av

(c) McGraw Hill Ryerson 2007

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.

See page 33

sms

h

km

m

h

km/21

3600

1

1

1000

1

75

Speed zone limits are stated in kilometres per hour (km/h).

(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.

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?

3. What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval?

See page 34

See next slide for answers

(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 34Take the Section 8.2 Quiz

Position-Time and Velocity-Time Graphs

Questions for ConsiderationWhat 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: timey-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

Position-Time Graphs

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

time (s)

posi

tion

(c

m)

Position-Time GraphsWhat are the

characteristics of this graph?Straight line, upward

slopeWhat kind of motion

created this graph?Constant speed 1 2 3 4 5 6 7 8 9 1

0

1

2

3

4

5

6

7

8

9

10

time (s)

posi

tion

(cm

)

Position-Time GraphsEach type of motion has a characteristic

shape on a P-T graph.Constant speedZero speed (at rest)Accelerating (speeding up)Decelerating (slowing down)

Position-Time GraphsConstant speed is represented by a straight

segment on the P-T graph.

time (s)p

os.

(m

)

Constant speed in positive direction.

time (s)p

os.

(m

)

Constant speed in negative direction.

Position-Time GraphsConstant speed is represented by a straight

segment on the P-T graph.

time (s)p

os.

(m

)

A horizontal segment means the object is at rest.

Position-Time GraphsCurved segments on the P-T graph mean

the object’s speed is changing.

time (s)p

os.

(m

)

Speeding up in positive direction.

time (s)p

os.

(m

)

Speeding up in negative direction.

Position-Time GraphsCurved segments on the P-T graph mean the

object’s speed is changing.

time (s)p

os.

(m

)

Traveling in positive direction, but slowing down.

time (s)p

os.

(m

)

Traveling in negative direction, but slowing down.

Position-Time GraphsThe slope of a P-T graph is equal to the

object’s velocity in that segment.

time (s)

posi

tion

(m

)

10 20 30 40

10

20

30

40

50 slope = change in ychange in x

slope = (30 m – 10 m)(30 s – 0 s)

slope = (20 m)(30 s)

slope = 0.67 m/s

Position-Time GraphsThe 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)

posi

tion

(m

)

N

S

Velocity-Time GraphsA 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!

Velocity-Time GraphsA horizontal line on the V-T graph means

constant velocity.

time (s)ve

loci

ty

(m/s

)

N

S

Object is moving at a constant velocity North.

Velocity-Time GraphsA horizontal line on the V-T graph means

constant velocity.

time (s)ve

loci

ty

(m/s

)

N

S

Object is moving at a constant velocity South.

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

time (s)ve

loci

ty

(m/s

)

N

S

Object is at rest

Velocity-Time GraphsIf 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.

Velocity-Time GraphsV-T graph has positive slope.

time (s)ve

loci

ty

(m/s

)

N

S Positive velocity and positive acceleration: object is speeding up!

time (s)ve

loci

ty

(m/s

)

N

S Negative velocity and positive acceleration: object is slowing down.

Velocity-Time GraphsIf 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.

Velocity-Time GraphsV-T graph has negative slope.

time (s)ve

loci

ty

(m/s

)

N

S Positive velocity and negative acceleration: object is slowing down,

time (s)ve

loci

ty

(m/s

)

N

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