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

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Ch. 8.2 Average Velocity

• 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.
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• Velocity ( ) is the displacement of an object
  divided by the time interval.
• In other words
• Velocity describes how fast an objects
• position is changing.
• Velocity is a vector quantity (direction).
• The units for velocity and speed are metres
• per second (m/s).

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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

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Finding the Slope of a Line

• Pick two points
• on the grid.
• 2. Make a triangle
• 3.
• 4. Units metres/second
• So slope 36.4 m/s

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Position Time Graph

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

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Example
Which joggers motion has a greater slope? Which
jogger is moving faster? What is the slope of
each line? What is each joggers ?
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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
  objects average velocity ( ).
• Average velocity is the rate of change in
  position for a time interval.

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• 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.

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• On a position-time graph if forward is given a
  positive direction
• A positive slope means that the objects average
  velocity is forward.
• A negative slope means that the objects average
  velocity is backwards.
• Zero slope means the objects average velocity is
  zero.

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Example 1
Calculating Average Velocity
The relationship between average velocity,
displacement, and time is given by

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

Solution Step One Write out known values.
Step Two Write down equation.
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Example 2

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

Solution Step One Write out known values.
Step Two Write down equation.
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Calculating Displacement
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

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Example 3

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

Solution Step One Write out known values.
Step Two Write down equation.
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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 runners
  displacement after 12 s?
• Answer 78 m West

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Calculating Time

• Use the last equation to solve the following
• How long would it take a cat walking north at
  0.80 m/s to travel 12 m north?
• Solution
• 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?

Solution
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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.

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Converting between m/s and km/h

• Try the following unit conversion problems
  yourself.
• 1. Convert 95 km/h to m/s.
• 95 km X 1000m X 1hr
• 1hr 1km 3600s
• A trucks displacement is 45 km north after
  driving for 1.3 hours. What was the trucks
  average velocity in km/h m/s?
• What is the displacement of an airplane flying
• 480 km/h E during a 5.0 min time interval?
  

26 m/s
Vav 45km 1.3hr
35 km/h N or 9.6 m/s N
40 km E or 40, 000 m E
d 480 km X .083 hr hr
Take the Section 8.2 Quiz