Describing Motion: Speed versus Velocity

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Describing MotionSpeed versus Velocity
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Speed distance timev d t

• Speed describes how fast something is moving. It
  is a scalar quantity (does NOT indicate
  direction)
• Example 1 At Monza, top speeds of almost
  350km/hr are the rule for Formula 1.
• Example 2 High speed elevators (like the ones in
  the CN Tower in Toronto), can attain a speed of
  7.11m/s.
• From these examples we can calculate the answer
  to other questions such as
• How much time would the CN tower elevator take to
  climb 37.5m (about 10 stories)?

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Manipulating the Equation

• Speed distance / time
• Distance speed x time
• Time distance / speed
• Equation Triangle d
• 
  v t

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Try These

• a) How far does a car travel if it moves at a
  speed of 50 km/h for 4.5 hours?
• b) How long does it take a rabbit to hop 500m if
  he can travel at an average speed of 2 m/s?
• c) How fast does a cyclist need to go in order to
  compete 12 km in 30 minutes?
• (record your answer in km/h)

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Time conversions

• We have already talked about and have been
  practicing Metric Conversions.
• In speed and velocity problems, because we are
  also working with TIME, we often need to convert
  the units of time.
• Complete the following
• 1 minute seconds
• 1 hour minutes
• 1 hour seconds

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Average vs. instantaneous speed

• Example As an object moves, it often undergoes
  changes in speed. For example, during an average
  trip to school, there are many changes in speed.
  Rather than the speed-o-meter maintaining a
  steady reading, the needle constantly moves up
  and down to reflect the stopping and starting and
  the accelerating and decelerating. One instant,
  the car may be moving at 50 km/hr and another
  instant, it might be stopped (i.e., 0 km/hr). Yet
  during the course of the trip to school the
  person might average 25 km/hr.

The average speed during the course of a motion
is often computed using the following
equation   Average speed total distance
traveled total time
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• Since a moving object often changes its speed
  during its motion, it is common to distinguish
  between the average speed and the instantaneous
  speed. The distinction is as follows.
• Instantaneous Speed - speed at any given instant
  in time.
• Average Speed - average of all instantaneous
  speeds found simply by a distance/time ratio.

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Velocity Speed with Direction
Velocity is a vector quantity which refers to
"the rate at which an object changes its
position."
Velocity displacement time
v d t
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Velocity Examples

• The physics teacher walks 4 meters East, 2 meters
  South, 4 meters West, and finally 2 meters North.
  The entire motion lasted for 24 seconds.
  Determine the average velocity.

Remember that the displacement refers to the
change in position and the velocity is based upon
this position change. In this case of the
teacher's motion, there is a position change of 0
meters and therefore an average velocity of 0
m/s.
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Describing Velocity

• Example Problem- Copy this into your notes

750m 1200m 600m
C A
B
D
A cross country skier starts at position A and
skies to B in 5 minutes. She turns and skies to C
in 12 minutes and then turns again and skies to D
where she stops after 20 minutes.
What is her average velocity (in m/s) once she
reaches B? C? and D?