Uniform Motion

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Uniform Motion
t (s) x (cm) v(cm/s)
0 0.0
1.0 5.0 5
2.0 10.0 5
3.0 15.0 5
4.0 20.0 5
5.0 25.0 5
6.0 30.0 5
7.0 35.0 5
8.0 40.0 5
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Non-uniform motion
t 1 s
t 3 s
t 9 s
t 0
t 2 s
t 4 s
t 5 s
t 8 s
t 6 s
t 7 s
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What is the velocity at t 5.5 s?
t 1 s
t 3 s
t 9 s
t 0
t 2 s
t 4 s
t 5 s
t 8 s
t 6 s
t 7 s

• All we know from the given data is the average
  velocity between t 5.0 and t 6.0 s.
• Measure the objects position at a smaller time
  interval, like t 5.4 s and t 5.6 s.
• Better yet, use t 5.49 s and t 5.51 s.
• The velocity at the instant t 5.5 s is
  approximately equal to the average velocity
  during a small time interval from t 5.49 s to t
  5.51 s. But the best we can do with the given
  data is guess.

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Instantaneous Velocity

• The velocity at an instant of time is called
  instantaneous velocity.
• It is approximately equal to the average velocity
  measured during a very small time interval.

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Position vs. time graph
t (s) x (cm)
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
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Position vs. time graph
t (s) x (cm)
0 0.0
1.0 0.5
2.0 2.2
3.0 5.0
4.0 8.8
5.0 13.8
6.0 19.9
7.0 27.2
8.0 35.4
9.0 45
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Position vs. time graph
-Slope of a tangent line on an x vs. t graph is
instantaneous velocity. -Sign of slope (pos or
neg) is direction of motion. -How slope changes
tells you whether it is speeding up or slowing
down.
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Example
Describe the motion of the object whose x vs. t
graph is shown below.
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Example
Describe the motion of the object whose x vs. t
graph is shown below.
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Velocity vs. time graph
t (s) x (cm) v(cm/s)
0 0.0
1.0 0.5 0.5
2.0 2.2 1.8
3.0 5.0 2.8
4.0 8.8 3.8
5.0 13.8 5.0
6.0 19.9 6.1
7.0 27.2 7.3
8.0 35.4 8.2
9.0 45 9.6
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Velocity vs. time graph
t (s) x (cm) v(cm/s)
0 0.0
1.0 0.5 0.5
2.0 2.2 1.8
3.0 5.0 2.8
4.0 8.8 3.8
5.0 13.8 5.0
6.0 19.9 6.1
7.0 27.2 7.3
8.0 35.4 8.2
9.0 45 9.6
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Velocity vs. time graph
-Slope of v vs. t graph is acceleration. -accelera
tion is the rate that the object speeds up or
slows down. -if slope is constant, then the
motion is characterized by constant acceleration
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Example
Describe the motion of the object whose v vs. t
graph is shown below.
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Example
Describe the motion of the object whose v vs. t
graph is shown below.
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Example
Describe the motion of the object whose v vs. t
graph is shown below.
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Observations
If the objects velocity is positive and the
object speeds up, its acceleration is

1. positive
2. negative
3. zero

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Observations
If the objects velocity is positive and the
object slows down, its acceleration is

1. positive
2. negative
3. zero

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Observations
If the objects velocity is negative and the
object slows down, its acceleration is

1. positive
2. negative
3. zero

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Observations
If the objects velocity is positive and the
object speeds up, its acceleration is

1. positive
2. negative
3. zero

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Poll
Position in meters
Car 1
t 1
t 2
t 3
t 4
t 0
Car 2
t 4
t 1
t 2
t 3
t 0
Car 3
t 0
t 1
t 2
t 4
t 3
Car 4
t 0
t 1
t 2
t 4
t 3
1. The positions of the cars above are shown at 1
s intervals from t 0 s to t 4 s. Which of
these cars have negative accelerations during
this 4 s time period?
A. Car 2 only B. Car 3 only C.
Car 4 only D. Cars 2 and 3 E. Cars 2 and
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Matching position and velocity graphs

1. Note what is being plotted in a given graph.
2. Describe the motion in words or with a diagram.
3. Sketch (or match) the graph that matches the
   motion diagram or verbal description of the
   motion.

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The graph at left shows a moving objects
velocity v vs clock reading t. One of the graphs
below shows the objects position x plotted vs t
over the same time interval. Which one is it?
v
0
t
A
B
C
x
x
x
0
0
0
t
t
t
D
E
x
x
0
0
t
t