Distance versus Displacement

Distance answers one question: how much ground did you cover? It adds up every step of a journey, no matter which way you turned. Walk in loops, backtrack, zigzag — it all piles onto the total. Displacement asks a different question: where did you end up, relative to where you started? It only cares about the start point and the end point, drawn as a straight arrow between them. Everything that happened in between is invisible to displacement, even if you wandered for miles.

This is why a runner can finish one full lap with sore legs and zero displacement: the path length is the whole track, but the start and end points are the same spot, so the arrow connecting them has zero length. A wandering path can rack up huge distance while the displacement arrow stays short, because distance keeps score of every meter walked while displacement only checks the net result. Displacement is not just distance with a direction stapled on — they can have completely different sizes, since distance never cancels and displacement can shrink to zero even after a long trip.

This distinction sets up everything else in the unit. Average speed uses distance over time, and average velocity uses displacement over time, so a round trip can have a healthy average speed but zero average velocity. Once position, displacement, and the sign conventions behind them feel solid, velocity and acceleration graphs build directly on the same idea of tracking net change versus total motion.