Position, displacement, and velocity

A GPS track, a stock chart, a sensor log — the first graph physics ever drew is still the most useful one: where something is, against time. Learn to read it and half of kinematics is already yours.

Position and displacement

Position x is where the object is, measured from an origin you choose. Displacement Δx = x₂ − x₁ is the change in position — a number with a sign. Walk 6 m forward and 6 m back and you've traveled 12 m, but your displacement is 0. Physics runs on displacement, because direction matters.

Velocity is a slope

Average velocity is displacement divided by the time it took:

$v_{avg} = \frac{\Delta x}{\Delta t}$

On a position–time graph, Δx is the rise and Δt is the run — so average velocity is literally the slope of the line connecting two points. That one sentence turns every motion question into a graph-reading question.

Three segments, three velocities, no formulas needed:

Instantaneous velocity

The speedometer doesn't show your average over the last hour — it shows your velocity right now. On a curved x–t graph, that's the slope of the tangent line at that instant: zoom in far enough and any smooth curve looks straight. (If you've met calculus: instantaneous velocity is the derivative of position. If you haven't, "slope at a point" is all you need here.)

Why this matters

Every graph in this course is read the same two ways — slope and area. You just learned the first half: the slope of x–t is velocity. The next lesson climbs one level: the slope of the velocity graph.