How to Determine Average Velocity & Average Acceleration

This lesson explains how to compute the average velocity and the average acceleration of an object moving along a line using definite integrals. You will learn how average value formulas apply to velocity and acceleration, and how direction, speed, and sign changes relate to these concepts.

Summary

The video reviews the relationships among position, velocity, and acceleration, and explains how to determine whether an object’s speed is increasing or decreasing. A detailed example shows how to find average velocity and average acceleration on a given interval both analytically and using Desmos. This skill is used frequently in AP Calculus free‑response and multiple‑choice questions.

Key Takeaways

• Average velocity is the definite integral of velocity divided by the width of the interval.

• Average acceleration is the definite integral of acceleration divided by the width of the interval.

• Velocity is the derivative of position; acceleration is the derivative of velocity.

• Positive velocity means motion to the right; negative velocity means motion to the left.

• Speed increases when velocity and acceleration have the same sign and decreases when they have opposite signs.

• To compute average acceleration, differentiate the velocity function to get acceleration.

• Desmos can compute integrals, derivatives, and average values quickly using built‑in functions.

• Correct notation and units are required when answering AP Calculus questions involving average value.