Position and Displacement

Position is a vector, r, that points from a chosen origin to wherever the object sits right now. It needs that origin and a coordinate system to mean anything: '5 meters' is meaningless until you say 5 meters from what, in which direction. Displacement, delta r, is just the change in that vector: r_final minus r_initial. It only cares about the two endpoints, not the road between them.

That is why a full lap of a track gives displacement zero. You left the starting line and you came back to it, so r_final equals r_initial and their difference vanishes, even though your legs covered real ground the whole time. Distance traveled adds up every bit of path length, always positive, always growing. Displacement can shrink, flip sign, or cancel out entirely, because it is a straight-line vector comparison of where you ended up versus where you began, not a record of the journey.

This sets up the rest of kinematics: velocity is defined as the rate of change of position, so it inherits displacement's vector nature, while speed is tied to distance the same way displacement is tied to position. Once motion becomes two-dimensional, position and displacement vectors get components, and you will track each axis separately before combining them. Sliding the origin shifts every position vector by a constant, but displacement, being a difference, stays exactly the same no matter where you put the origin.