📚

All Subjects

>

♾️

AP Calc

>

🐶

Unit 8

# 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals Anusha Tekumulla

### AP Calculus AB/BC♾️

Bookmarked 7.6k • 259 resources
See Units

🎥AP Calculus AB/BC - Position, Velocity, and Acceleration
Motion problems are very common throughout calculus. With derivatives, we calculated an object's velocity given its position function. With integrals, we go in the opposite direction: given the velocity function of a moving object, we find out about its position or about the change in its position. 🚘

## How do we use Integrals to Connect Position, Velocity, and Acceleration? 🧩

When integrating the acceleration function, you will get the velocity function. When integrating the velocity function, you will get the position function. This concept is essential to understand when learning about the applications of integration. When you have an indefinite integral of a function, the result will be the function that comes before it. ↩️

## Integration is Going Backwards

In essence, using integrals for PVA (position, velocity, acceleration) problems is just the opposite of derivation. If you're given a velocity function and need to position, just integrate! This is because of the fundamental theorem of calculus.

### The College Board stresses the importance of this topic in integral calculus: ❗️

"For a particle in rectilinear motion over an interval of time, the definite integral of velocity represents the particle’s displacement over the interval of time, and the definite integral of speed represents the particle’s total distance traveled over the interval of time." ## Resources:

Thousands of students are studying with us for the AP Calculus AB/BC exam.
#####   Studying with Hours = the ultimate focus mode
Start a free study session
##### 🔍 Are you ready for college apps?
Take this quiz and find out!
Start Quiz
Browse Study Guides By Unit
📆Big Reviews: Finals & Exam Prep
✍️Free Response Questions (FRQ)
🧐Multiple Choice Questions (MCQ)
Unit 10: Infinite Sequences and Series (BC Only)
👑Unit 1: Limits & Continuity
🤓Unit 2: Differentiation: Definition & Fundamental Properties
🤙🏽Unit 3: Differentiation: Composite, Implicit & Inverse Functions
👀Unit 4: Contextual Applications of the Differentiation
Unit 5: Analytical Applications of Differentiation
🔥Unit 6: Integration and Accumulation of Change
💎Unit 7: Differential Equations
🐶Unit 8: Applications of Integration
🦖Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)
#####  FREE AP calc Survival Pack + Cram Chart PDF
Thousands of students are studying with us for the AP Calculus AB/BC exam.
##### 💪🏽 Are you ready for the Calc AB exam?
Take this quiz for a progress check on what you’ve learned this year and get a personalized study plan to grab that 5!
START QUIZ
##### 💪🏽 Are you ready for the Calc BC exam?
Take this quiz for a progress check on what you’ve learned this year and get a personalized study plan to grab that 5!
START QUIZ
##### Play this on HyperTyper
Practice your typing skills while reading Connecting Position, Velocity, and Acceleration of Functions Using Integrals
Start Game  