Directed Distance
Directed distances are distances with a direction or sense. They can be determined along straight lines and along curved lines. A directed distance along a straight line from A to B is a vector joining any two points in a n-dimensional Euclidean vector space. A directed distance along a curved line is not a vector and is represented by a segment of that curved line defined by endpoints A and B, with some specific information indicating the sense (or direction) of an ideal or real motion from one endpoint of the segment to the other (see figure). For instance, just labelling the two endpoints as A and B can indicate the sense, if the ordered sequence (A, B) is assumed, which implies that A is the starting point.
A displacement (see above) is a special kind of directed distance defined in mechanics. A directed distance is called displacement when it is the distance along a straight line (minimum distance) from A and B, and when A and B are positions occupied by the same particle at two different instants of time. This implies motion of the particle. displace is a vector quantity.
Another kind of directed distance is that between two different particles or point masses at a given time. For instance, the distance from the center of gravity of the Earth A and the center of gravity of the Moon B (which does not strictly imply motion from A to B).Shortest path length may be equal to displacement or may not be equal to.Distance from starting point is always equal to magnitude of displacement. For same particle distance travelled is always greater than or equal to magnitude of displacement. Shortest path length is not necessary always displacement.Diplacement may increase or decrease but distance travelled never decreases.
Read more about this topic: Distance, Distance Versus Directed Distance and Displacement
Famous quotes containing the words directed and/or distance:
“In history the great moment is, when the savage is just ceasing to be a savage, with all his hairy Pelasgic strength directed on his opening sense of beauty;—and you have Pericles and Phidias,—and not yet passed over into the Corinthian civility. Everything good in nature and in the world is in that moment of transition, when the swarthy juices still flow plentifully from nature, but their astrigency or acridity is got out by ethics and humanity.”
—Ralph Waldo Emerson (1803–1882)
“The particular source of frustration of women observing their own self-study and measuring their worth as women by the distance they kept from men necessitated that a distance be kept, and so what vindicated them also poured fuel on the furnace of their rage. One delight presumed another dissatisfaction, but their hatefulness confessed to their own lack of power to please. They hated men because they needed husbands, and they loathed the men they chased away for going.”
—Alexander Theroux (b. 1940)