What JSD has said about position and location already being vector
quantities is undoubtedly true in a formal mathematical sense, but I suspect
most people (including physicists) don't really think of position formally
as a vector quantity. We do realize that our position it is relative to
some reference point and deep down that does imply a direction but that is
not the way we really consider position (and almost certainly not the way
students do). As I sit here in South Bend, Indiana, I don't consider my
location in terms of a direction (other than perhaps that this is Northern
Indiana). Late next week I will be in Chicago. Again I have a rough
feeling for the position of Chicago, but I really only put a strong
directional notion to this when I consider going FROM South Bend TO Chicago.
I now envision a DISPLACEMENT of about 120 miles, mostly West but also a
little North. I think that _operationally_, that's what happens with the
definition of Displacement = change in position. We consider the positions
themselves without direction but construct the vector from the initial
position to the final position (as opposed to subtracting two 'position
vectors'.) In other words, right or wrong, there is a strong tendency to
consider location or position as scalar quantities and displacement as the
vector quantity that is constructed (not using vector subtraction) from the
positions. In intro courses where students have no background in vectors
and where one is NOT going to really teach vectors, this seems like a useful
approach towards the concept of velocity.
Rick
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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu
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