average velocity

Average velocity smooths a whole trip into a single steady velocity that would have carried you from start to finish in the same time. It ignores every bump, stop, and burst of speed along the way and just asks: where did you end up, how long did it take, and in what direction was the net change? It is the 'if this journey had been done at one constant velocity, what would it have been?' number.

Precisely, average velocity is the displacement divided by the time interval: v_avg = delta x / delta t = (x_final - x_initial) / (t_final - t_initial). Because it uses displacement (a vector), average velocity has a direction and a sign, and it can be zero even after a long trip if you return to where you started. On a position-time graph, the average velocity between two instants is the slope of the straight line joining those two points.

The honest catch is that average velocity uses only the endpoints — it is blind to everything in between. Two very different journeys with the same start point, end point, and duration have identical average velocity. That is why it can be zero for a round trip (displacement zero) even though you were never actually standing still. To capture the moment-to-moment motion you need instantaneous velocity instead.