Motion Graphs in 1D

Intro

Graphs are where AP Physics starts to separate strong reasoning from formula reflexes. This week is about reading motion graphs as stories with slope, area, and sign meaning built into them.

Core Lesson

A position-time graph tells you where an object is and how that position changes; its slope represents velocity. A velocity-time graph tells you how velocity changes with time; its slope represents acceleration, and the signed area under it represents displacement.

The most common mistake is confusing slope with height. On a velocity-time graph, the height tells you velocity, but the area tells you displacement. On a position-time graph, the height tells you position, but the slope tells you velocity.

Read graphs in layers. First read the graph directly. Then ask what the slope means. Then ask what the area means, if area is relevant. That order keeps you from grabbing the wrong interpretation.

AP Lift

Modern AP questions love graph translation. Students are expected to move between graph, table, sentence, and physical interpretation without treating graphs as decoration. If slope and area are not automatic, later units get much harder.

Must-Master Objectives

• Interpret slope on position-time and velocity-time graphs.
• Interpret signed area on a velocity-time graph.
• Match graph shapes to motion stories.
• Explain why graph height and graph slope represent different ideas.

Problem Set Prompts

1. On a position-time graph, what does a horizontal line mean physically?
2. On a position-time graph, what does a straight line with negative slope mean?
3. A velocity-time graph stays above zero and slopes downward toward zero. Describe the motion.
4. A velocity-time graph is a horizontal line at -2 m/s. What is the acceleration?
5. If the area under a velocity-time graph from 0 to 4 s is 6 m, what does that tell you?
6. A position-time graph curves upward and gets steeper with time. What can you infer about the velocity?
7. A velocity-time graph crosses from positive to negative. What event likely happened?
8. Sketch a velocity-time graph for an object moving right, slowing down, stopping, and then moving left faster and faster.
9. Stretch: Give two different motion stories that could produce the same position-time graph over a short interval.

Reflection Prompt

• When you look at a graph, do you first read its shape or hunt for numbers?
• Which graph idea still trips you most often: slope, area, or sign?