Using Calculus to Understand Motion

Calculus is the language of motion. Physics uses derivatives to analyze how objects move, and integrals to find distances traveled.

Velocity and Acceleration

• Velocity is the derivative of position: how fast and in what direction something moves.
• Acceleration is the derivative of velocity: how quickly speed changes.

Real-World Applications

• Predicting where a car will be after a set time.
• Calculating how far a rocket travels in a given period.

Integrals for Distance

Integrating the velocity function gives total distance traveled, even if speed varies.