Answer to Question #113921 in Atomic and Nuclear Physics for Angela

Question

Say you are walking around the track and you stop at the same point where you started.How would you describe the distance you walked be your displacement

Answer 1

Distance is a scalar measure of the interval between two locations measured along the actual path connecting them.

Displacement is a vector measure of the interval between two locations measured along the shortest path connecting them.

So, if I started my way at point $p$ and ended at the same point, then I probably walked along a closed curve $\gamma: [0,1] \to S,\,\, \gamma(0)=\gamma(1)=p$. Hence, the distance will be equal to the length $l(\gamma)$ of this curve, but my displacement will be zero.