January 17, 2026

AP Physics 1: Motion Graphs Master Guide

A triptych showing position vs. time, velocity vs. time, and acceleration vs. time graphs side-by-side for an object with constant positive acceleration.

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AP Physics 1: Motion Graphs Master Guide

Exam Tip: Approximately 50% of Kinematics MCQ questions involve analyzing a graph. You must be able to read “slope” and “area” instantly.

1. Position vs. Time Graphs (x vs. t)

This graph tells you where an object is located.

Three separate position vs. time graphs showing: an object at rest, an object with constant velocity, and an accelerating object.
How to read the shape of a Position vs. Time graph. Steepness equals speed; curvature equals acceleration.
[Image of position vs time graph]
Slope = Velocity If slope is steep, it’s fast. If horizontal, it’s stopped.
Shape = Acceleration
  • Straight Line: Zero Acceleration (Constant v)
  • Curved (Happy Face \cup): Positive Acceleration
  • Curved (Frown \cap): Negative Acceleration

2. Velocity vs. Time Graphs (v vs. t)

This is the most important graph on the AP Exam because it links everything together.

A velocity vs. time graph showing a diagonal line. The slope is annotated as acceleration, and the shaded area underneath is annotated as displacement.
The “Master Graph.” On a v-t graph, the slope tells you acceleration, and the shaded area tells you how far it moved (displacement).
[Image of velocity vs time graph]

Slope = Acceleration

Steep slope = High acceleration.
Horizontal line = Constant velocity (a=0).

Area = Displacement

The “Area Under the Curve” (between the line and the x-axis) tells you how far it moved (\Delta x).

The “Crossing the Axis” Rule: Whenever the graph crosses the horizontal axis (goes from + to – or vice versa), the object has changed direction.

3. Acceleration vs. Time Graphs (a vs. t)

In AP Physics 1, this graph is almost always a series of flat horizontal lines (because we deal with constant acceleration).

  • Read the Value: Tells you the acceleration at that moment.
  • Area Under Curve: Tells you the Change in Velocity (\Delta v).

4. AP-Style Concept Checks

Test your ability to read graphs without using a calculator. These are typical multiple-choice style concepts.

Question 1 (Velocity Graph): An object moves along the x-axis. Its velocity vs. time graph is a straight diagonal line starting at v = -10 \, \text{m/s} and ending at v = +10 \, \text{m/s}. Describe the motion.

▶ Click to see Answer

Answer: The object slows down while moving left, stops momentarily, and then speeds up moving right.

Reasoning:

  • Start: Negative velocity means moving left.
  • Middle: The line crosses the axis at v=0. This means it stops.
  • End: Positive velocity means moving right.
  • Slope: The constant positive slope means constant positive acceleration the whole time.

Question 2 (Position Graph): Two cars, A and B, are moving along a straight road. On a Position vs. Time graph, Car A’s line is steep and negative. Car B’s line is shallow and positive. Which car is moving faster?

▶ Click to see Answer

Answer: Car A is faster.

Reasoning: Speed is determined by the magnitude (steepness) of the slope, not the direction. Car A has a steeper slope, so it covers more meters per second, even though it is moving in the negative direction.

Question 3 (The “Frown” Rule): An object’s Position vs. Time graph is shaped like an upside-down parabola (a frown \cap). The object is moving in the positive direction. Is the object speeding up or slowing down?

▶ Click to see Answer

Answer: Slowing down.

Reasoning:

  • Velocity: The slope is positive (moving positive direction).
  • Acceleration: The shape is a “frown” (concave down), which means acceleration is negative.
  • Conclusion: When velocity (+) and acceleration (-) have opposite signs, the object slows down.

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