Motion: A Math Model Introduction

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Motion A Math ModelIntroduction

• Graphing Motion in 1 dimension

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Motion in one dimension

• Now that you have Read/Studied/taken notes on one
  dimensional motion in terms of words, sketches
  and motion diagrams, and displayed them such as
  with dots on ticker tape as well as with vectors,
  well now examine representing such information
  by means of graphs.

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Displacement

• Displacement defined as the change in position
  of an object.
• Displacement vs time graphs are very important
  for describing and recording position and change
  in position.

• Position Vs Time

Slope is the velocity
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Velocity (constant)

• Velocity defined as change in position or
  displacement divided by the change in the time
  over which the position changes. When the
  position change is constant, so is the velocity.

• Velocity Vs Time

Constant Velocity
Change in position is constant
Slope velocity
Area under the graph shows displacement
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Velocity (uniform acceleration)

• Velocity defined as change in position or
  displacement divided by the change in the time
  over which the position changes. When the
  position change increases by a constant amount so
  does the velocity.

• Velocity Vs Time

Velocity with uniform acceleration
Slope acceleration Area under graph is velocity
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Velocity (non-uniform acc.)

• Velocity defined as change in position or
  displacement divided by the change in the time
  over which the position changes. When the
  position change varies, so does the velocity.

• Velocity Vs Time

Slope at a point is acceleration at that moment.
While area under graph is the displacement.
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Uniform Acceleration

• Acceleration defined as the change in velocity
  divided by the time interval over which the
  change occurs. When the velocity changes by a
  constant amount there is uniform acceleration.

• Acceleration Vs Time

Velocity increases by a constant amount.
Area under the graph is the velocity.
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• Acceleration defined as the change in velocity
  divided by the time interval over which the
  change occurs. When the velocity change varies
  there is not uniform acceleration.

• Acceleration Vs Time

Velocitys change is changing by a non-constant
amount
Area under graph is velocity