just think about the example i gave you and think of any other ones you can think of..... the displacement will never be greater than the distance.
Think of distance as "distance travelled"
So if you're going from point A to point B in any situation you can think of (around curves, over mountains etc...) The distance travelled will be greater because you had travel "around" things.
The displacement is a straight line between point A and B, so it is always the shortest possible distance.
Strictly speaking, distance is a magnitude but displacement is a vector.
So, yoiu really mean
"why is distance >= magnitude of displacement ?"
Mathematically,
[tex] \int \left| d\vec s \right| \geq \left| \int d\vec s \right| [/tex]
Essentially, distance [ the arc-length of a curve from A to B ] is the sum of non-negative quantities.
The magntude of displacement [ the magnitude of a vector from A to B ] is the non-negative magnitude of a sum-of-(signed)-vector-quantities.
The proof of the inequality is essentially the triangle inequality.
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