Constant Velocity and the
Shape of P-T Graphs

Constant Velocity
• Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s.
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Graph of Constant Velocity
• If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right.
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Constant Velocity
• Motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a positiontime graph.
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Shape Principle
• The shapes of the position vs. time graphs for these two basic types of motion reveal an important principle.
• Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa).
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Shape Principle
• 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).
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Example 1
• This graph shows an object which is moving with a positive velocity (positive slope), a constant velocity (constant slope) and a small velocity (small slope).
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Example 2
• The graph on the right has similar features constant, positive velocity (the constant, positive slope).
However, the slope of this graph is larger.
This larger slope is indicative of a larger velocity.
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Describe the Motion
• Negative Velocity
• Constant Velocity
• Slow Velocity
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Compare the Motion
• Negative Velocity
• Constant Velocity
• Faster Velocity
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IMPORTANT NOTE!
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Check Your Understanding
• Use the principle of slope to describe the motion of the objects depicted. In your description, be sure to include such information as the direction of the velocity
(i.e., positive or negative), and whether the object is moving slow, fast, speeding up, or slowing down. Be complete in your description.
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Interpretation of p-t Graphs
• Recall:
– On a p-t graph a negative slope means that the object is moving in the negative direction.
– A positive slope means that the object is moving in the positive direction.
– No slope (zero) means that the object is at rest.
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Interpretation of p-t Graphs
• Example:
– A dog trainer throws a stick, the dog chases and covers
15 meters in 3 seconds.
– The dog then sits on command, 15 meters away from the trainer for 3 seconds.
– The dog approaches 10 meters in 2 seconds, then sits and waits for another 2 seconds.
– The dog then comes right to the trainer’s feet and sits for
2 seconds.
Position (m) vs Time (s)
16
14
12
10
8
6
4
2
0
1 3 5 7 9 11 13
Time (s)
Position (m)
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Try This!
• Write out a “story” that explains this graph.
Position (m) vs Time (s)
-5
-10
-15
5
0
20
15
10
1 2 3 4 5 6 7 8 9 10 11
Time (s)
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