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.