A position vs time graph plots an object's position (vertical axis) against time (horizontal axis), so the slope at any point equals the object's velocity and the curvature tells you whether the object is accelerating. It's a core motion representation in AP Physics 1 Topic 1.2.
A position vs time graph (often written x vs t) shows where an object is at every moment. Time runs along the horizontal axis, position along the vertical axis. The graph treats the object as a single point, which is exactly the object model from the CED (1.2.A.1), so you ignore size and shape and just track one location.
Here's the part that actually matters on the exam. The graph's slope IS the velocity. A steep line means fast motion, a flat line means the object is sitting still, and a negative slope means it's moving in the negative direction. The change in the vertical value between two times is the displacement, Δx = x − x₀ (1.2.A.2), and rise over run gives you average velocity, v_avg = Δx/Δt (1.2.B.2). A straight line means constant velocity. A curved line means the velocity is changing, which means the object is accelerating (1.2.B.4). So a position-time graph is really a velocity detector in disguise. You read it with your eyes on the slope, not the height.
This term lives in Topic 1.2 (Representations of Motion) in Unit 1: Kinematics, and it directly supports learning objectives 1.2.A (describe a change in an object's position) and 1.2.B (describe the average velocity and acceleration of an object). AP Physics 1 is built around translating between representations of the same motion, including graphs, equations, motion diagrams, and words. The position-time graph is usually the first translation skill you learn, and everything in Unit 1 builds on it. If you can't read slope as velocity, the rest of kinematics (and later, the motion caused by forces in Unit 2) gets much harder. Graph interpretation also shows up constantly in both multiple-choice questions and FRQs, so this is one of the highest-payoff skills in the course.
Keep studying AP Physics 1 Unit 1
Velocity vs Time Graph (Unit 1)
These two graphs describe the same motion from different angles. The slope of the position-time graph at any instant gives the value plotted on the velocity-time graph at that instant. Learning to convert one into the other is a classic AP skill, and the most common mistake is reading a position graph as if it were a velocity graph.
Displacement (Unit 1)
Displacement is just the change in the vertical reading on a position-time graph, Δx = x − x₀. If the graph ends at the same height it started, the displacement is zero even if the object traveled a long path. That's the displacement vs distance distinction made visual.
Acceleration (Unit 1)
Curvature is the giveaway. A straight position-time line means zero acceleration; a curve means the slope (velocity) is changing, so the object is accelerating (1.2.B.4). A parabola on a position-time graph is the signature of constant acceleration.
Free Fall (Unit 1)
A dropped object's position-time graph is a parabola because gravity provides constant acceleration. Free fall is the standard example the exam uses to test whether you can connect a curved x-t graph to constant acceleration of magnitude g.
AP Physics 1 tests this term through interpretation, not memorization. Multiple-choice stems hand you an x vs t graph and ask things like which interval has the greatest speed (steepest slope), when the object is at rest (flat slope), when it changes direction (slope flips sign, meaning the graph hits a peak or valley), or which velocity-time graph matches it. FRQs often ask you to sketch a position-time graph from a description of motion or from a v-t graph, then justify your sketch in words. No released FRQ needs to use the phrase verbatim for this to matter; graph translation is baked into the kinematics questions every year. The skills to drill are reading slope as velocity, computing v_avg = Δx/Δt between two points, and recognizing that curvature means acceleration.
On a position-time graph, the height tells you WHERE the object is and the slope tells you how fast it's going. On a velocity-time graph, the height tells you how fast it's going and the slope tells you the acceleration. The classic trap is a graph crossing the time axis. On an x-t graph, crossing zero just means the object passed the origin. On a v-t graph, crossing zero means the object momentarily stopped and reversed direction. Always check the vertical axis label before you read anything.
The slope of a position vs time graph at any point equals the object's velocity at that moment, with rise over run giving v_avg = Δx/Δt (CED 1.2.B.2).
A flat (horizontal) section means the object is at rest, not that it has zero position.
A straight line means constant velocity, while a curved line means the velocity is changing, so the object is accelerating (CED 1.2.B.4).
The object changes direction wherever the graph has a peak or valley, because that's where the slope switches sign.
Displacement is the change in the vertical value between two times (Δx = x − x₀), which can be zero even if the object moved a lot.
Never confuse it with a velocity-time graph; the height of an x-t graph is location, not speed.
It's a graph with time on the horizontal axis and an object's position on the vertical axis, used in Topic 1.2 (Representations of Motion). Its slope at any moment equals the object's velocity, and its curvature reveals acceleration.
Yes. A horizontal segment means the position isn't changing, so the velocity (the slope) is zero and the object is at rest. It does not mean the object is at the origin; that only happens where the graph touches the time axis.
On a position-time graph the slope gives velocity, while on a velocity-time graph the slope gives acceleration. They show the same motion, but a line crossing zero means passing the origin on an x-t graph and momentarily stopping on a v-t graph.
Yes. A curve means the slope is changing, and since slope equals velocity, a changing slope means changing velocity, which is the CED's definition of accelerating (1.2.B.4). A parabola specifically signals constant acceleration, like free fall.
Calculate the slope. For average velocity over an interval, use v_avg = Δx/Δt, the change in position divided by the change in time (CED 1.2.B.2). For velocity at a single instant on a curved graph, find the slope of the tangent line at that point.
Connect this key term to the AP exam workflow: review the course, practice questions, and check related study tools.
Review units, study guides, and course resources.
Check this vocabulary in multiple-choice context.
Apply key concepts in written AP responses.
Estimate the exam score you are working toward.
Review the highest-yield facts before practice.
Put the full course together before test day.