Displacement
Displacement is a vector quantity, commonly
denoted by the vector s,
that reflects an object’s change in spatial position. The displacement
of an object that moves from point A to
point B is a vector whose tail is
at A and whose tip is at B.
Displacement deals only with the separation between points A and B,
and not with the path the object followed between points A and B.
By contrast, the distance that the object travels is
equal to the length of path AB.
Students often mistake displacement for distance, and
SAT II Physics may well call for you to distinguish between the
two. A question favored by test makers everywhere is to ask the displacement
of an athlete who has run a lap on a 400-meter track.
The answer, of course, is zero: after running a lap, the athlete
is back where he or she started. The distance traveled by the athlete,
and not the displacement, is 400 meters.
Example
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Alan
and Eva are walking through a beautiful garden. Because Eva is very
worried about the upcoming SAT II Physics Test, she takes no time
to smell the flowers and instead walks on a straight path from the west
garden gate to the east gate, a distance of 100 meters. Alan, unconcerned
about the test, meanders off the straight path to smell all the
flowers in sight. When Alan and Eva meet at the east gate, who has walked
a greater distance? What are their displacements? |
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Since Eva took the direct path between the west and east
garden gates and Alan took an indirect path, Alan has traveled a
much greater distance than Eva. Yet, as we have discussed, displacement
is a vector quantity that measures the distance separating the starting point
from the ending point: the path taken between the two points is
irrelevant. So Alan and Eva both have the same displacement: 100 meters
east of the west gate. Note that, because displacement is a vector
quantity, it is not enough to say that the displacement is 100 meters:
you must also state the direction of that displacement. The distance
that Eva has traveled is exactly equal to the magnitude of her displacement:
100 meters.
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After
reaching the east gate, Eva and Alan notice that the gate is locked,
so they must turn around and exit the garden through the west gate.
On the return trip, Alan again wanders off to smell the flowers,
and Eva travels the path directly between the gates. At the center
of the garden, Eva stops to throw a penny into a fountain. At this
point, what is her displacement from her starting point at the west
gate? |
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Eva is now 50 meters from the west gate,
so her displacement is 50 meters, even though she has
traveled a total distance of 150 meters.
When Alan and Eva reconvene at the west gate, their displacements
are both zero, as they both began and ended their garden journey
at the west gate. The moral of the story? Always take time to smell
the flowers!
