Motion and Force

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Motion and Force
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Chapter Three Motion

• 3.1 Position and Velocity
• 3.2 Graphs of Motion
• 3.3 Acceleration

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Investigation 3B
Position, Speed and Time Graphs

• What kind of motion happens when an object rolls
  down a hill?

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3.2 The position vs. time graph

• Motion graphs are an important tool used to show
  the relationships between position, speed, and
  time.

A runner can learn more about performance by
studying data and graphs.
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3.2 The position vs. time graph

• Position vs. time data tells you the runners
  position at different points in time.
• The runner is at 50 meters after 10 sec., 100
  meters after 20 sec. and 150 meters at 30 sec.

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3.2 Graphs show relationships

• A good way to show a relationship between two
  variables is to use a graph.
• A graph makes it easy to see if changes in one
  variable cause changes in the other variable (the
  effect).

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3.2 The position vs. time graph

• To graph data, you put position on the vertical
  (y) axis .
• Time goes on the horizontal (x) axis.
• Data are plotted between x and y axis.

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3.2 The position vs. time graph

• An object moving at a constant speed always
  creates a position vs. time graph that is a
  straight line.

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3.2 The position vs. time graph

• Two variables may have
• a strong relationship,
• a weak relationship,
• or no relationship at all.

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3.2 Graphs show relationships

• This table shows how quickly the car gets from A
  to B as the angle of the track changes.

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3.2 Graphs show relationships

• If we plot the data on a graph, what kind of
  relationship does the graph show?

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3.2 Four steps to make a graph

• Step 1 Choose which will be the dependent and
  independent variables. The dependent variable
  goes on the y-axis and the independent variable
  goes on the x-axis.
• Step 2 Make a scale for each axis by counting
  boxes to fit your largest value. Count by
  multiples of 1, 2, 5, or 10.
• Step 3 Plot each point by finding the x-value
  and drawing a lin upward until you get to the
  right y-value.
• Step 4 Draw a smooth curve that shows the
  pattern of the points. Do not just connect the
  dots.

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3.2 Reading a graph

• A graph can give you an accurate answer even
  without doing the experiment.
• Students doing an experiment measured the speed
  of the car at 20, 40, 60, and 80 cm positions.
• They want to know the speed at 50 cm.

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3.2 Slope

• You can use position vs. time graphs to quickly
  compare the speeds of different objects.

A steeper line on a position vs. time graph means
a faster speed.
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3.2 Slope

• The steepness of a line is called its slope.
• Visualize a triangle with the slope as the
  hypotenuse.
• The rise is equal to the height of the triangle.
• The run is equal to the length along the base of
  the triangle.

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3.2 Slope

• The slope is the ratio of the rise (vertical
  change) to the run (horizontal change).
• The slope is therefore a distance divided by a
  time, which equals speed.

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3.2 Speed vs. time graphs

• The position vs. time graph has position on the
  y-axis and time on the x-axis.

Which runner has the fastest constant speed?
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3.2 Speed vs. time graphs
These graphs each show the same event. What
differences do you notice?
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Do these graphs display the same data?
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3.2 Calculating distance

• A speed vs. time graph can also be used to find
  the distance the object has traveled.