A position-time graph plots position, x, on the vertical axis against time, t, on the horizontal axis. Every point on the line is a snapshot:
To read the position at a specific time, find that time on the horizontal axis, trace straight up (or down) to the line, then trace straight across to the vertical axis. That's it — no formula needed, just careful reading.
The shape of the line between two points carries the real story. A line that rises means position is increasing — the object is moving away from the origin. A line that falls means position is decreasing — the object is moving back toward the origin. A flat line means position isn't changing at all — the object is at rest.
The steepness of the line — how much it rises or falls per second — tells you how fast the object is moving. A steep line covers a lot of position change in a little time: fast. A gentle slope covers only a little position change over the same time: slow. This steepness is exactly what you'll formalize as velocity once you have signed numbers in Lesson 1-1-3.
This graph tells the story of a cyclist. Drag the time slider and watch the dot move along the line — and along the number line below it.
A position-time graph shows a line going from the point (2 s, 3 m) to the point (6 s, 15 m). Describe the motion during this interval.
When two lines share the same axes, you can compare the two objects directly. Whichever line is steeper at a given moment belongs to the faster object at that moment. And wherever the two lines cross, something specific happens.
That object is moving faster right now — regardless of which one is ahead in position.
Same x, same t for both lines — the two objects are in the same place at the same instant.
The real test of fluency: can you translate a written motion story into a graph, and can you go the other direction just as easily?
'A student starts at the classroom door (x = 0 m). She walks quickly to her locker at x = 12 m, taking 4 s. She stands at her locker for 6 s. Then she walks slowly back toward the door, but only makes it to x = 4 m by the time the bell rings 8 s later.' Sketch this as a position-time graph.
You've been describing direction in words — "away from," "back toward." In Lesson 1-1-3, you'll replace those words with a plus or minus sign, and the slope of a position-time graph will officially become velocity rather than just "steepness with a direction word attached." Everything you practiced today about rising, falling, and flat lines carries over directly — you're just about to get a much more precise vocabulary for it.