Describing Motion with Position vs. Time Graphs

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Describing Motion with Position vs. Time Graphs
The specific features of the motion of objects
are demonstrated by the shape and the slope of
the lines on a position vs. time graph.
To begin, consider a car moving with a constant,
rightward () velocity of 10 m/s.
Note that a motion with constant, positive
velocity results in a line of constant and
positive slope when plotted as a position-time
graph.
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The Principle of Slope for a positiontime Graph
The shapes of the position vs. time graphs for
these two basic types of motion constant
velocity motion and changing velocity motion
(i.e.accelerated motion) reveal an important
principle.
The principle is that the slope of the line on a
position-time graph reveals useful information
about the velocity of the object. It's often
said, "As the slope goes, so goes the velocity."
If the velocity is constant, then the slope is
constant (i.e., a straight line). If the velocity
is changing, then the slope is changing (i.e., a
curved line). If the velocity is positive, then
the slope is positive (i.e., moving upwards and
to the right). If the velocity is negative, then
the slope is negative (i.e., Moving downward to
the right).
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Slow, Rightward () Constant Velocity
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Positive Velocity Zero Acceleration
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Fast, Rightward () Constant Velocity
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Slow, Leftward () Constant Velocity
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Fast, Leftward () Constant Velocity
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Leftward () Velocity Slow to Fast
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Leftward () Velocity Fast to Slow
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Now consider a car moving with a changing,
rightward () velocity that is, a car that is
moving rightward and speeding up or accelerating.
Note that a motion with changing, positive
velocity results in a line of changing and
positive slope when plotted as a position-time
graph.
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Positive Velocity Constant Velocity
Positive Velocity Changing Velocity
(acceleration)
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The Passing Lane position vs. time graph
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The Passing Lane Velocity vs. Time Graph
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The Stoplight
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Two-Stage Rocket
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Consider a car moving with a constant velocity of
10 m/s for 5 seconds. The diagram below depicts
such a motion.
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Consider a car moving with a constant velocity of
5 m/s for 5 seconds, stopping abruptly, and then
remaining at rest (v 0 m/s) for 5 seconds.
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1. Consider the graph at the right. The object
whose motion is represented by this graph is ...
(include all that are true)
a. moving in the positive direction. b. moving
with a constant velocity. c. moving with a
negative velocity.
d. slowing down.
e. changing directions.
f. speeding up.
g. moving with a positive acceleration. h. moving
with a constant acceleration.
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Determining the Area on a velocity-time Graph
1. A plot of velocity vs. time can be used to
determine the acceleration of an object (slope
acceleration).
2. A plot of velocity vs. time can also be used
to determine the distance traveled by an object
3. For velocity vs. time graphs, the area bounded
by the line and the axes represents the distance
traveled.
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The shaded area is representative of the distance
traveled by the object during the time interval
from 0 seconds to 6 seconds. This representation
of the distance traveled takes on the shape of a
rectangle whose area can be calculated using the
appropriate equation.
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The shaded area is representative of the distance
traveled by the object during the time interval
from 0 seconds to 4 seconds. This representation
of the distance traveled takes on the shape of a
triangle whose area can be calculated using the
appropriate equation.
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The shaded area is representative of the distance
traveled by the object during the time interval
from 2 seconds to 5 seconds. This representation
of the distance traveled takes on the shape of a
trapezoid whose area can be calculated using the
appropriate equation.
Calculating the Area