• Speed ( ) is the distance an object travels divided by the time to travel that distance.

• In other words

– Speed is a scalar quantity (no direction).

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

v

t

dv

Ch. 8.2 Average Velocity

• Velocity ( ) is the displacement of an object divided by the time interval.• In other words

• Velocity describes how fast an object’s position is changing.

•Velocity is a vector quantity (has a direction).

•The units for velocity and speed are metres per second (m/s).

t

dv

v

Calculating the Slope of the Position-Time Graph

• To learn more about velocity, we must now understand straight line graphs.

• The slope of a graph is represented by

– rise = change in y-axis– run = change in x-axis

runrise

Finding the Slope of a Line1. Pick two points

on the grid.

2. Make a triangle

3.

4. Units = metres/second

So slope = 36.4 m/s

4.3611

400

run

riseslope

0 2 4 6 8 10 12 14 16 18 20

500

400

300

200

100

Posi

tion (

m)

Time (s)

11

400

Position – Time Graph

• On a position-time graph the slope is the change in position ( ) divided by the change in time ( ).

t

d

slope

d

t

Example

Which jogger’s motion has a greater slope?Which jogger is moving faster?What is the slope of each line?What is each jogger’s ?avv

On a position-time graph if “forward” is given a positive direction:

• A positive slope means that the object’s average velocity is forward.

• A negative slope means that the object’s average velocity is backwards.

• Zero slope means the object’s average velocity is zero.

HOLD IT!

• Time to complete ‘slope worksheet’ assignment

Position – Time Graph

• On a position-time graph the slope is the change in position ( ) divided by the change in time ( ).

t

d

slope

d

t

• Remember , (average velocity), is a vector and we must therefore always include a direction.

• If we were to discuss , (average speed), we do not need to include direction, because speed is a scalar.

avv

avv

Average Velocity• Usually, objects do not move at a perfectly constant speed.• For this reason, we often use “average velocity” in our

calculations. • The slope of a position-time graph is the object’s average

velocity ( ).• Average velocity is the rate of change in position for a time

interval. avv

HOLD IT!

• Homework (in workbook)

• #1-5 pg.157• #1-3 pg.158-9• #1-2 pg.160-1

Step Three: Insert values into equation

s

forwardmv

0.4

14

SolutionStep One: Write out known values.Step Two: Write down equation.Step Four: Calculate answer.

?

4

14

v

st

forwardmd

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

v av

d

t

Example 1

forwardsmv /5.3

1. What is the average velocity of a dog that takes 4.0 s to run forward 14 m?

Calculating Average Velocity

v av

d

t

Solution

Step One: Write out known values.

Step Two: Write down equation.

Step Three: Insert values into equation

s

Eastmv

120

280

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

Step Four: Calculate answer.Eastsmv /3.2

Example 2

?

120

280

v

st

Eastmd

v av

d

t

][/33.2 Esmv

v av

d

t

The formula for finding velocity can be rearranged so that you can solve for either displacement or time.

You can solve for time by taking this equation and divide both sides by leaving the equation:

Calculating Displacement

avv

avv

d

t

Step Four: Calculate answer.Step Three: Insert values into equation

150.8

15][/0.8

dor

sNsmd

Solution

Step One: Write out known values.Step Two: Write down equation.

Example 3

smv

st

d

/0.8

15

?

t avvd

1. What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s?

][120 Nmd

Example 4

Solve this problem on your own, using the same steps.

4.A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s?

Answer: 78 m West

Calculating TimeUse the last equation to solve the following:

1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north?

Solution:

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?

avv

d

t

st 15

st 73.0Solution:

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.

sms

h

km

m

h

km/21

3600

1

1

1000

1

75

Try the following unit conversion problems yourself.

1. Convert 95 km/h to m/s. • 95 km X 1000m X 1hr

1hr 1km 3600s

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 & m/s?

3. What is the displacement (in m & km) of an airplane flying

480 km/h [E] during a 5.0 min time interval? d = 480 km X .083 hr hr

Vav = 45km

1.3hr

Converting between m/s and km/h

Take the Section 8.2 Quiz

= 26 m/s

= 35 km/h N or 9.6 m/s N

40 km [E] or 40, 000 m [E]

HOLD IT!

• Homework (in workbook)

• #1-3 pg.156