# Ch 31: Calculus Applications: Velocity & Acceleration

### About This Chapter

## Calculus Applications: Velocity & Acceleration - Chapter Summary

The informative lessons in this chapter explain velocity and acceleration as they're used in calculus. Your study includes the definition and formula used for acceleration, the equation used for velocity and the comparison between rate of change and velocity. Other topics include how displacement of an object is determined using velocity and time. Once you complete these lessons, you should be ready to:

- Use the equation for vertical velocity
- Calculate acceleration due to gravity using a formula
- Analyze linear motion using differentiation
- Compare acceleration and velocity as functions

Getting ready for a test is easy with our professionally designed and self-paced learning tools. You can watch any of our video lessons as many times as you need to in order to fully understand the material. Use the video tabs feature to skip ahead or go back to review any specific topic in a video. Then take the multiple-choice quizzes following each lesson to see how well you'll do on your test.

### 1. What is Acceleration? - Definition and Formula

This lesson describes the difference between speed, velocity and acceleration. Examples are used to help you understand the concept of acceleration and learn to calculate acceleration with a mathematical formula.

### 2. Velocity in Math: Definition, Equation & Problems

Velocity in math is similar to speed, with only one difference. Learn what that difference is, how to write velocity, and how to calculate velocity problems.

### 3. Velocity and the Rate of Change

Running from your little sister or just window-shopping, your speed is just a measure of how fast you move, or how your position is changing over time. In this lesson, learn about how velocity is a rate of change.

### 4. Velocity vs. Time: Determining Displacement of an Object

There is a lot of information you can determine by looking at a velocity vs. time graph. In this lesson, we will use a little geometry to calculate the displacement of the object represented by the graph.

### 5. Vertical Velocity: Definition & Equation

In this lesson we will look at vertical velocity and why it is very different from horizontal velocity. You will learn the equation used to calculate vertical velocity and learn to apply it to a few situations.

### 6. Calculating Acceleration Due to Gravity: Formula & Concept

You have no doubt seen gravity work in your life. After all, it is the force that keeps your feet on the ground! This lesson explores the acceleration a body experiences due to gravity and provides details of the mechanics behind it.

### 7. Using Differentiation to Analyze Linear Motion

Derivatives have many practical applications, including modeling linear motion. In this lesson, learn how to use differentiation to analyze linear motion by finding the velocity and acceleration of a moving particle.

### 8. Velocity & Acceleration as Functions

The velocity and acceleration of a particle can be expressed as mathematical functions of time. In this lesson, you will learn about how these functions are developed and how to use them.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the HSC Mathematics: Exam Prep & Syllabus course

- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Integration
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards