Read and reason
Length of path versus change of place
A person walks 6 m east, turns around, and walks 6 m west. The total distance is 12 m because all traveled path segments count. Their displacement is final coordinate minus initial coordinate: 0 m if they arrive exactly where they started. Distance is a nonnegative scalar; displacement is a signed quantity in this one-dimensional model, carrying direction.
Average velocity has a sign
Average velocity is Δx/Δt. If a walker starts at 5 m and ends at −1 m after 3 s, Δx = −1 − 5 = −6 m and average velocity = −2 m/s. The negative sign says motion was toward decreasing x for the net interval. Average speed instead divides total distance by total elapsed time. When the path includes a reversal, average speed and magnitude of average velocity generally differ.
From a graph to a story
A position–time plot can show a rising straight segment, a level segment, and a falling segment. The slope of each straight segment reports velocity for that interval. A level segment indicates no change in position; a downward segment indicates velocity in the negative coordinate direction. The graph is not a map of the physical trail—it shows position against time. A curve's shape has a mathematical interpretation, not an overhead picture of the route.
Check every unit
Distance and displacement use meters, speed and velocity use meters per second, and acceleration uses meters per second squared. Never report an average velocity in meters without dividing by seconds. Always keep track of whether a comparison is across a whole interval or at an instant. Averages do not automatically tell you what happened at every moment between measurements.