Motion and Force

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Motion and Force
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Chapter Three Motion

• 3.1 Position and Velocity
• 3.2 Graphs of Motion
• 3.3 Acceleration

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Investigation 3A
Positive and Negative Position

• How do we measure position in two dimensions?

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3.1 The position variable

• Motion is about knowing where things are and how
  they move.
• To understand where things are, we need to
  understand position.

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3.1 The position variable

• Position is a variable and it is always relative
  to an origin, or the place where the objects
  starting point was zero.

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3.1 Forward and backward

• Position and distance are similar but not the
  same.
• Both use units of length.
• Distance can have only positive values.

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3.1 Forward and backward

• Position uses positive and negative numbers.
• Positive numbers are for positions to the right
  (in front) of the origin.
• Negative numbers are for positions to the left
  (or behind) the origin.

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3.1 Forward and backward

• Many variables can be positive or negative.
• These include position, speed, and force.
• These variables are called vectors because they
  can have a value and a direction.

We use the term velocity to mean speed with
direction.
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3.1 Keeping track of where you are

• Pathfinder is a small robot sent to explore Mars.

• It landed on Mars in 1997.
• Where is Pathfinder now?

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3.1 Keeping track of where you are

• Pathfinder keeps track of its velocity vector and
  uses a clock.
• Suppose Pathfinder moves forward at 0.2 m/s for
  10 seconds.

What is Pathfinders velocity?
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3.1 Keeping track of where you are

• Suppose Pathfinder goes backward at 0.2 m/s for 4
  seconds.

What is Pathfinders velocity?
What is Pathfinders change in position?
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3.1 Keeping track of where you are

• The change in position is the velocity multiplied
  by the time.

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3.1 Keeping track of where you are

• Each change in position is added up using
  positive and negative numbers.
• Pathfinder has a computer to do this.

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3.1 Maps and coordinates

• If Pathfinder was crawling on a straight board,
  it would have only two choices for direction.

• Out on the surface of Mars, Pathfinder has more
  choices. The possible directions include north,
  east, south, and west, and anything in between.

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3.1 Maps and coordinates

• Pathfinders exact position can be described with
  two numbers.
• These numbers are called coordinates.

• This graph shows Pathfinder at coordinates (4, 2)
  m.

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3.1 Maps and coordinates

• The graph can also show any path Pathfinder
  takes, curved or straight.

• This kind of graph is called a map.
• Street maps often use letters and numbers for
  coordinates.

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3.1 Vectors on a map

• Suppose you run east for 10 seconds at a speed of
  2 m/s.
• Then you turn and run south at the same speed for
  10 more seconds.

• Where are you compared to where you started?