---
title: "Position vs Time Graph — AP Physics 1 Definition & Guide"
description: "A position-time graph plots position vs. time, where slope gives velocity and curvature reveals acceleration. Essential for AP Physics 1 Unit 1 kinematics."
canonical: "https://fiveable.me/ap-physics-1-revised/key-terms/position-versus-time-graph"
type: "key-term"
subject: "AP Physics 1"
unit: "Unit 1"
---

# Position vs Time Graph — AP Physics 1 Definition & Guide

## Definition

A position versus time graph plots an object's position (vertical axis) against time (horizontal axis); the slope at any point equals the object's velocity, and the curvature signals acceleration, so a concave-up curve with an initially negative slope means negative initial velocity with positive acceleration.

## What It Is

A position versus time graph (often written x-t graph) is one of the core representations of motion in [AP Physics 1](/ap-physics-1-revised "fv-autolink"). [Position](/ap-physics-1-revised/key-terms/position "fv-autolink") goes on the vertical axis, time on the horizontal axis, and the curve traces where the object is at every moment. The single most important skill is reading the **slope**. Slope on an x-t graph is velocity, period. A steep line means fast, a flat line means stopped, and a negative slope means the object is moving in the negative direction.

Curvature carries the second layer of information. A straight line means constant velocity (zero [acceleration](/ap-physics-1-revised/unit-1/5-vectors-and-motion-in-two-dimensions/study-guide/LvdiAzU3amzMqu6O "fv-autolink")). A curved line means the velocity is changing, so the object is accelerating. Concave up means acceleration points in the positive direction; concave down means it points in the negative direction. That's why a concave-up curve that starts with a negative slope describes an object initially moving in the negative direction while slowing down, momentarily stopping at the bottom of the curve, then speeding up in the positive direction. Think of it like a ball thrown downward onto a trampoline, with the bounce-back built into one smooth curve.

## Why It Matters

This term lives in [Topic 1.3](/ap-physics-1-revised/unit-1/3-representing-motion/study-guide/3s3qyB2ey6r2Q1UI "fv-autolink") (Representing Motion) in [Unit 1](/ap-physics-1-revised/unit-1 "fv-autolink"): Kinematics, and it directly supports learning objective 1.3.A, which asks you to describe the position, velocity, and acceleration of an object using representations of its motion. Essential knowledge 1.3.A.1 lists graphs alongside motion diagrams, equations, and narrative descriptions as the official ways motion can be represented, and the x-t graph is the one that shows up most often. Translating between an x-t graph and the constant-acceleration kinematic equations (1.3.A.2) is a foundational AP Physics 1 skill. A parabolic x-t graph is literally the equation x = x₀ + v₀t + ½at² drawn as a picture. If you can read slope and curvature fluently, you can describe motion without doing a single calculation, and that's exactly what many exam questions test.

## Connections

### Velocity versus time graph (Unit 1)

The two graphs are linked by slope and area. The slope of the x-t graph at any instant is the value plotted on the v-t graph at that instant, and the area under the v-t graph gives the [displacement](/ap-physics-1-revised/unit-1/2-displacement-velocity-and-acceleration/study-guide/HyscWF2F28uakfpc "fv-autolink") shown on the x-t graph. The exam loves asking you to sketch one graph from the other.

### Kinematic equations for constant acceleration (Unit 1)

Under [constant acceleration](/ap-physics-1-revised/key-terms/constant-acceleration "fv-autolink"), the x-t graph is a parabola described by x = x₀ + v₀t + ½at². The y-intercept is initial position, the initial slope is v₀, and the curvature direction matches the sign of a. The graph and the equation are the same physics in two languages.

### Free fall near Earth's surface (Unit 1)

An object in [free fall](/ap-physics-1-revised/key-terms/free-fall "fv-autolink") has constant downward acceleration, so its position-time graph is always concave down (with up as positive). A ball thrown upward traces a concave-down parabola whose peak marks the instant velocity equals zero, even though acceleration never does.

### Energy and work graphs (Units 3-4)

The graph-reading habits you build here transfer directly. Later in the course you'll pull meaning from slopes and areas on force-position and energy graphs, and the skill of asking 'what does the slope mean physically?' starts with the x-t graph.

## On the AP Exam

Position-time graphs are a multiple-choice staple in Unit 1. Typical stems show you an x-t graph and ask when the object is moving fastest, when it changes direction, or which v-t graph matches. The trap answers always punish students who read the graph's height instead of its slope. On the free-response side, AP Physics 1 regularly includes graphing and translation tasks where you sketch a position-time graph from a description, a motion diagram, or a velocity-time graph, then justify features like curvature in words. Be ready to say things like 'the slope is zero at t = 2 s, so the object is momentarily at rest' rather than just drawing the curve. Connecting the graph to a verbal description of velocity and acceleration is exactly what LO 1.3.A asks for.

## position versus time graph vs Velocity versus time graph

The axes look identical at a glance, so students constantly misread one as the other. On an x-t graph, slope is velocity and the curve crossing zero means the object passes through the origin. On a v-t graph, slope is acceleration and the curve crossing zero means the object changes direction. A flat line on an x-t graph means the object is stopped; a flat line on a v-t graph means it's cruising at constant velocity. Before you read any kinematics graph on the exam, check the vertical axis label first. That one habit prevents most graph errors.

## Key Takeaways

- On a position versus time graph, the slope at any point equals the object's instantaneous velocity.
- A straight line means constant velocity, while a curved line means the object is accelerating.
- Concave up means positive acceleration and concave down means negative acceleration, regardless of which way the object is currently moving.
- An object changes direction at the point where the x-t graph has zero slope, like the bottom of a concave-up curve.
- A concave-up curve with an initially negative slope shows an object moving in the negative direction while slowing, stopping, then moving in the positive direction.
- For constant acceleration, the x-t graph is a parabola that matches the equation x = x₀ + v₀t + ½at².

## FAQs

### What does a position versus time graph show in AP Physics 1?

It shows an object's position at every moment in time, with position on the vertical axis and time on the horizontal axis. The slope gives velocity and the curvature reveals acceleration, supporting learning objective 1.3.A in Unit 1.

### Does the height of a position-time graph tell you how fast an object is moving?

No. Height tells you where the object is, not how fast it's going. Speed comes from the slope, so an object can be far from the origin (high on the graph) while sitting completely still on a flat section.

### How is a position-time graph different from a velocity-time graph?

On a position-time graph, slope means velocity and zero slope means the object is at rest. On a velocity-time graph, slope means acceleration and crossing the time axis means the object changes direction. Always check the vertical axis label before interpreting anything.

### What does a concave-up curve with negative initial slope mean on an x-t graph?

The object starts out moving in the negative direction (negative initial velocity) while experiencing positive acceleration. It slows down, momentarily stops at the lowest point of the curve, then speeds up in the positive direction.

### Why is a position-time graph curved for an object in free fall?

Free fall means constant acceleration from gravity, so velocity changes every instant and the slope of the x-t graph keeps changing. The result is a parabola, which matches the kinematic equation x = x₀ + v₀t + ½at² with a as the acceleration due to gravity.

## Related Study Guides

- [1.3 Representing Motion](/ap-physics-1-revised/unit-1/3-representing-motion/study-guide/3s3qyB2ey6r2Q1UI)

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