Graphing Motion

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Graphing Motion

• Physics 11

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Some humour to start..
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Cartesian Coordinates

• Often use the Cartesian plane in order to
  identify an objects position when describing
  motion
• Same as the x-y plane used math class

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Uniform Motion

• Predicting the behaviour of moving objects can be
  very complex. Measuring and analyzing motion in
  the real world is a challenge, so scientists try
  to simplify their task.
• Scientists often try to model the behaviour of
  objects that move in almost straight lines at
  almost constant speed as uniform motion because
  this can be easily analyzed.
• Uniform motion motion at constant velocity, with
  no change in speed or direction.

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General rules to follow when graphing

• Independent variable goes on the x-axis
• Dependent variable goes on the y-axis
• Always label your axis so you know what they
  represent
• Add a title to your graph
• Draw a line of best fit if necessary

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Lines of Best Fit

• Best fit means to have an equal number of points
  above and below the line and equidistant from the
  line
• This represents the average of the plotted points

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Position-time graphs

• shows the position of an object over time
• X-axis time
• Y-axis position
• The slope of a position-time
• graph is the velocity!!!!!

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Position-Time Graphs
Displacement (m) Vs. Time (sec.)
Displacement
20
1
2
40
60
3
80
4
100
5
120
6
140
7
160
8
180
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Position-Time Graph
Displacement (m) Vs. Time (sec.)
Rise
Or
Run
Slope df di tf - ti
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Position-Time Graph
Displacement (m) Vs. Time (sec.)
The constant slope indicates that the velocity of
the object remains constant
The Slope of this Line Remains Constant
Throughout the Graph
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Position-Time Graph
Displacement (m) Vs. Time (sec.)
The velocity of this object changes over time..
C
B
A
In which section is the object moving the fastest?
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For position-time graphs showing uniform motion,
then

• There are only three possible shapes for the
  graphs to take
• No motion, object is stationary
• d
• 3. Uniform motion to the left (backward)
• t d
• 2. Uniform motion to the right (forward)
• d
• t
• t

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(No Transcript)
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Lets graph

• At the Berlin Marathon in 2008, Ethiopian Haile
  Gebrselassie set a new world record for the
  marathon with a time of 20359. The key to
  Gebrselassies success is his ability to maintain
  a constant pace through out the event. His split
  times for each 5km interval (and half marathon
  and marathon splits) are given below.

d(km) t(s)
0 0
5 875
10 1753
15 2643
20 3530
21.1 3725
25 4421
30 5307
35 6185
40 7054
42.2 7439
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1. Using the data table, plot his position (d) on
   the y-axis and his time (t) on the x-axis.
   Ensure that you choose a scale that will enable
   you to use as much of the graph paper as
   possible.
2. Using the data, draw a line of best fit to the
   data and determine the slope of the line.
3. What are the units for the slope in this
   instance?
4. For each 5km split (you can ignore the 21.1km and
   42.2km) calculate his average speed (velocity) in
   m/s by dividing the distance in metres by the
   time in seconds.
5. Compare the results for your slope calculation to
   your results from question 4. What do you
   notice? What you can say about his pacing?

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Some more practise

• WS