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.
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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
- 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