Position–Time Graphs
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
On a position–time graph, the height tells you where the object is, and the slope tells you its velocity: steeper means faster, and the sign of the slope gives the direction.
1. How to read a position–time graph
2. Straight lines and curves
A straight line has one slope, so the velocity is constant: no speeding up, no slowing down. That’s true even if the line slopes downward.
A curved line has a changing slope, so the velocity is changing. To find the velocity at one instant, look at how steep the curve is right at that point (the slope of a tangent line).
3. Example, then try it
Use the graph below. What is the velocity during segment C, and what is the displacement from 0 to 7 s?
v = Δx ÷ Δt = (0 − 6 m) ÷ (7 − 4 s) = −2 m/s
It starts at x = 0 and ends at x = 0, so the displacement is 0. (The distance traveled is 6 + 6 = 12 m.)
In the graph below, find the cart’s velocity in each part, and its average velocity from 1 s to 8 s.
First part (slope): v = (14 − 2) m ÷ (5 − 1) s = 12 ÷ 4 = +3 m/s
Flat part: slope = 0, so v = 0. The cart sits at x = 14 m.
Average velocity: vavg = Δx ÷ Δt = (14 − 2) m ÷ (8 − 1) s = 12 ÷ 7 ≈ +1.7 m/s
Answer: +3 m/s, then 0 m/s; average velocity ≈ +1.7 m/s. (Not 1.5 m/s: the two parts last different amounts of time, so you can’t just average 3 and 0.)
4. Common mistakes
An object’s position–time graph is a horizontal line at x = 5 m. What is the object doing?
A horizontal line has zero slope, so the velocity is zero. The height tells you where it sits: x = 5 m.
Ready to practice?
5 questions on Position–Time Graphs, each with a hint and an explanation for every wrong answer.