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In addition to the revision notes for Displacement and Distance in 2 and 3 Dimensions on this page, you can also access the following Kinematics learning resources for Displacement and Distance in 2 and 3 Dimensions
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 3.4 | Displacement and Distance in 2 and 3 Dimensions |
In these revision notes for Displacement and Distance in 2 and 3 Dimensions, we cover the following key points:
Displacement represents the shortest path between two points in a line, plane or space while Distance is the length of the true path followed by the object during its motion. Displacement can be shorter or equal to the Distance but it cannot be longer.
In two dimensions, if the initial position of the moving object is the vector r⃗1 and the its final position is the vector r⃗2, we can write for the displacement ∆r⃗
Splitting the vectors in components, we obtain
and
Therefore, the magnitude of the Displacement vector ∆r⃗ is
When an object is moving in space, we call it "3D motion." In this case, an additional coordinate (usually denoted by z) is required to represent the third dimension.
However, the approach is the same as for 2D motion. We simply write the z-coordinate besides the x- and y-coordinates and all calculations rely on these three coordinates.
Thus, if the vector r⃗i shows the initial position and the vector r⃗f the final position of the object in space, both them have three coordinates each: xi, yi and zi for r⃗i and xf, yf and zf for r⃗f. Therefore, the displacement vector
will have three coordinates as well. They are:
The magnitude of the Displacement vector ∆r⃗ therefore is
Or
Conceptually, there is nothing new here; the only difference with the study of 2-D motion is the new coordinate z, which makes the equations longer, but the structure is the same.
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