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 fordistance, and
SAT II Physics may well call for you to distinguishbetween the two. A question favored by test makers everywhere is to askthe displacement of an athlete who has run a lap on a 400-metertrack. The answer, of course, is zero: after running a lap, the athleteis back where he or she started. The distance traveled by the athlete,and not the displacement, is 400 meters.
Example
Alan and Eva are walking through abeautiful garden. Because Eva is veryworried about the upcoming SAT IIPhysics Test, she takes no time tosmell the flowers and instead walkson a straight path from the westgarden gate to the east gate, adistance of 100 meters. Alan,unconcerned about the test, meanders offthe straight path to smell allthe flowers in sight. When Alan and Evameet at the east gate, who haswalked a greater distance? What aretheir displacements?
Since Eva took the direct path between thewest and east garden gates and Alan took an indirect path, Alan hastraveled a much greater distance than Eva. Yet, as we have discussed,displacement is a vector quantity that measures the distance separatingthe starting point from the ending point: the path taken between thetwo points is irrelevant. So Alan and Eva both have the samedisplacement: 100 meters east ofthe west gate. Note that, because displacement is a vector quantity, itis not enough to say that the displacement is 100 meters: you must alsostate the direction of that displacement. The distance that Eva hastraveled is exactly equal to the magnitude of her displacement: 100meters.
After reaching the east gate, Eva and Alannotice that the gate islocked, so they must turn around and exit thegarden through the westgate. On the return trip, Alan again wandersoff to smell the flowers,and Eva travels the path directly between thegates. At the center ofthe garden, Eva stops to throw a penny into afountain. At this point,what is her displacement from her startingpoint at the west gate?
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 westgate, their displacements are both zero, as they both began and endedtheir garden journey at the west gate. The moral of the story? Alwaystake time to smell the flowers!
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本帖最后由 端木·宇 于 2008-6-19 20:22 编辑 ]
