Displacement

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Displacement
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Distance is a scalar quantity and tells you only
the magnitude (number sum only) of a path taken.
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Displacement is the shortest distance between the
starting point and the end point.
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Distance vs. Displacement

• You drive the path, and your odometer goes up by
  8 miles (your distance).
• Your displacement is the shorter directed
  distance from start to stop (yellow arrow).
• What if you drove in a circle?

start
stop
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Explanation

• Distance is the actual length measured of a
  particular path taken.
• Displacement is the length and direction of a
  straight line drawn from the start to finish.

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Why does it matter?
Explanation

• Why does one need to understand and use distance
  vs displacement?
• Travel
• Taxis driver should operate such that distance
  is as close to displacement as possibleotherwise
  youre being taken on the scenic (and more
  expensive) route
• Directions a kind local informing you that the
  museum youve been searching for is only a few
  blocks from here doesnt help unless they
  include direction

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Explanation

• The most important distinction between distance
  and displacement is that distance is a scalar
  and displacement is a vector.
• Scalars are simple magnitudes.
• 15 apples
• 135 miles
• Vectors contain information about the magnitude
  (size) and direction of a physical observable.
• 64 miles Southwest
• Vectors are typically depicted as arrows drawn
  with a specific length and pointing in a specific
  direction.

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Explanation

• Units of distance?
• Symbol is d
• Units of displacement?

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Explanation

• Mass
• Scalar or Vector?
• Units?
• Distance
• Scalar or Vector?
• Units?
• Displacement
• Scalar or Vector?
• Units?
• Time
• Scalar or Vector?
• Units?

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Elaboration

• A car travels 6 miles East and then 8 miles
  North.
• Determine the distance traveled by the car.
• Draw and describe (magnitude and direction) the
  displacement vector of the car.

So the cars displacement is 10 miles 53o N of E
10 mi
8 mi N
53o N of E
6 mi E
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Distance vs. Displacement HO 1.5
Evaluation
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Summary of Concepts
Conclusion

• Distance is the length of the path traveled.
• Displacement (from dis-place to dat-place) is
  the length and direction of a line from start to
  finish.
• Position is a location relative to a point of
  reference.
• Displacement is a vector quantity that contains
  both magnitude and direction.