How come the displacement vector for an object moving in 2D be longer than the length of path traveled by the object over the same time interval but not less than?
2006-10-22 10:17:31 · 2 answers · asked by sleepy 1 in Science & Mathematics ➔ Physics
So its the other way around, how come it can be less than but NOT greater than?
2006-10-22 10:36:41 · update #1
No way I can think of. Displacement can be less than or equal to path length but not greater than. Displacement is the straight-line, minimum-length measurement of position after some specified motion. See the ref.
To answer your followup: They both go from the same start point to the same end point. Displacement is the shortest possible measurement of the position change, whereas the path can be curved and/or otherwise complicated (which makes it longer than displacement) or also straight-line and minimum-distance (which makes it equal to displacement), but it can't be shorter than "shortest possible".
2006-10-22 10:31:48 · answer #1 · answered by kirchwey 7 · 1⤊ 0⤋
I think you have this back to front as
| x1 + x2 + x3 + ,,,,,, + xn | ≤ | x1| + | x2 | + | x3 | + ,,,,,, + | xn |
meaning the size of the resultant vector is less than or equal to the sum of the sizes of the individual vectors and the equality only occurs when all the vectors are in a line and heading in the same direction.
2006-10-22 10:41:40 · answer #2 · answered by Wal C 6 · 0⤊ 0⤋