Transcript Slide 1

Motion and Force
Chapter Three: Motion
• 3.1 Position and Velocity
• 3.2 Graphs of Motion
• 3.3 Acceleration
Investigation 3B
Position, Speed and Time Graphs
• What kind of motion happens when an
object rolls down a hill?
3.2 The position vs. time graph
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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.
3.2 The position vs. time graph
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Position vs. time data
tells you the runner’s
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.
3.2 Graphs show relationships
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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).
3.2 The position vs. time graph
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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.
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.
3.2 The position vs. time graph
• Two variables may have:
– a strong relationship,
– a weak relationship,
– or no relationship at all.
3.2 Graphs show relationships
•
This table shows
how quickly the
car gets from A to
B as the angle of
the track changes.
3.2 Graphs show relationships
•
If we plot the data
on a graph, what
kind of relationship
does the graph
show?
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 xaxis.
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.
3.2 Reading a graph
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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.
3.2 Slope
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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.
3.2 Slope
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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.
3.2 Slope
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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.
3.2 Speed vs. time graphs
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The position vs.
time graph has
position on the
y-axis and time
on the x-axis.
Which runner has the fastest constant speed?
3.2 Speed vs. time graphs
These graphs each show the same event.
What differences do you notice?
Do these graphs display the same data?
3.2 Calculating distance
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A speed vs. time graph can also be used to find
the distance the object has traveled.