1.1 Displacement, Distance, Speed, and Velocity

For motion constrained to a straight line, position is represented by one coordinate. You can use x for horizontal motion or y for vertical motion, but the logic is the same: the coordinate tells you where the object is relative to your chosen origin.

Because position is directional, we treat it as a vector quantity even in one dimension. In practice, that means positive and negative coordinates carry physical meaning rather than being mere arithmetic signs.

Distance is different: it is the total path length traveled. If direction changes during motion, distance and the magnitude of displacement are no longer equal. A round trip can have large distance but zero displacement.

This distinction matters in every average-rate calculation. Whenever the path has turns or reversals, always compute displacement and distance separately before moving to velocity or speed.

In one-way motion without reversal, average speed and the magnitude of average velocity are equal. Once direction changes, they split: average speed stays positive and is usually larger in magnitude than average velocity.

For constant velocity motion, position changes linearly with time. The position-time graph is a straight line whose slope is velocity. The velocity-time graph is a horizontal line, and the signed area under that velocity-time graph over an interval is the displacement in that interval.