Distance and Displacement

Summary

• Displacement…
  • is a vector measure of the spatial interval between two locations measured along the shortest path connecting them.
  • may be described…
    • with a magnitude (∆s) and a direction (θ) or
    • as a set of components (∆x, ∆y).
  • is represented by the symbol ∆s (boldface).
  • is synonymous with a change in position.
• Distance…
  • is a scalar measure of the spatial interval between two locations measured along the actual path connecting them.
  • has magnitude only.
  • is represented by the symbol ∆s (italic).
• Symbols
  • The origin of the symbols for displacement (∆s) and distance (∆s) is spatium, the Latin word for space (like the space between two locations).
• The relation of distance to displacement
  • The distance traveled to get from one location to another is always greater than or equal to the magnitude of the displacement between the two locations.

    ∆s ≥ |∆s|

  • Distance approaches the magnitude of displacement as distance approaches zero.

    ∆s → 0

    ⇒

    ∆s → |∆s|

• The SI unit of distance and displacement is the meter [m].
  • The meter is one of the seven base units of the International System of Units.