Connecting Position, Velocity, & Acceleration

This lesson explains how to connect position, velocity, and acceleration using derivatives and integrals, and analyze motion along a line using.

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

• The derivative of position is velocity, and the derivative of velocity is acceleration.

• Positive velocity means the object is moving to the right, and negative velocity means it is moving to the left.

• Positive acceleration means velocity is increasing, while negative acceleration means velocity is decreasing.

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

• Intervals of motion are determined by analyzing the sign of the velocity function.

• Velocity is increasing or decreasing based on the sign of the acceleration.

• Average velocity over an interval can be found using the integral of velocity or by using change in position over time.

• Velocity can be expressed as an integral of acceleration when an initial velocity is given.

Transcript

All right guys, Mr. Antonucci here, and in this third video of three we’re going to talk about how to connect position, velocity, and acceleration of an object along a line. We can often use the first derivative test to investigate properties of motion of an object on a line. We talked about this a little bit in the previous video, but I’m going to review it here to make sure it’s fresh.