Motion in One Dimension (Position vs. Time) Chapter 5.1

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Motion in One Dimension (Position vs.
Time)Chapter 5.1
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Distance, Position and Displacement

• Distance The total distance that an object has
  moved.
• Ex. You walk 3 meters north and then walk 3
  meters south. What distance have you traveled?
• 6 meters

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Distance, Position and Displacement

• Position Where you are relative to a starting
  point.
• Ex. You walk 3 meters north.
• Your position is 3 meters from your starting
  point.

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Distance, Position and Displacement

• Displacement A measure in distance relative to a
  starting point that includes direction.
• Ex. You walk 3 meters north and then 3 meters
  south. What is your displacement?
• 0 meters.
• Ex. Your walk 3 meters north and 4 meters east.
  What is your distance traveled? What is your
  displacement?
• Distance 7 meters.
• Displacement 5 meters.

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Motion of Objects

• To describe the motion of an object, what other
  information will we need other than position,
  distance or displacement?
• Time
• If I have the objects position and time, what
  can be determined about the objects motion?
• Speed or Velocity

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1. Collect Data
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2. Choose appropriate axes and plot the data.
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3. Draw a curve that provides a best fit to the
points.
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What information does the shape of the curve
provide?

• Straight line constant velocity.
• Changing curve changing velocity(i.e.
  acceleration).

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What information does the shape of the curve
provide?
Negative Acceleration
Positive Acceleration
Decreasing Velocity
Increasing Velocity
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Characterize the motion of the object from A to E.

1. Constant velocity in the positive direction.
2. Decreasing velocity.
3. Stationary.
4. Increasing velocity.
5. Constant velocity in the positive direction.

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What information does the slope of the curve
provide?

• Positively sloped curve movement in the
  positive direction.
• Negatively sloped curve movement in the
  negative direction.

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What else does the slope tell us?

• What is the motion described by each curve?
• How does the velocity of each curve compare to
  one another?
• A is stationary
• B is moving at the same
• speed as C, but their starting
• position is different.
• D is moving slower than
• B or C.

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Analyzing motion of more than one object.

• Two vehicles travel through a speed trap
  traveling at two different velocities.

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Determining the slope of the curve.
1997 World Championships - Athens, Greece
Maurice Green
100
90
80
70
60
Distance (m)
50
40
30
20
10
0
0
2
4
6
8
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Time (s)
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Velocity determined from the slope of the curve.
rise run df di tf
ti 85m-50m 8.4s-5.4s m 11.7m/s Since
m v v 11.7 m/s
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Key Ideas

• Although space exists in 3 dimensions, analysis
  of objects in motion can be limited to one
  dimension to simplify problems.
• When graphing position vs. time, use the x-axis
  for time and the y-axis for position.
• By analyzing the shape of a position vs. time
  graph, the relative motion of the object can be
  determined, i.e. constant velocity, acceleration,
  stationary.
• The slope of the position vs. time graph provides
  the average velocity over the time interval.

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What can be inferred from the following graph?