Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Derivatives
Subtopic: Motion and the Derivative

Overview

Calculus is the study of change and motion. Derivatives are one way of quantifying motion. In today's lesson we use the derivative to study motion, in particular position, velocity, and acceleration. These are important applications of the first and second derivative especially to physics and biology majors.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.3.1 Understand the difference between average velocity and instantaneous velocity and know which is given by the derivative
• 2.3.2 Understand the position function and its notation
• 2.3.3 Understand the height function and its notation
• 2.3.4 Given a position function, find the velocity and acceleration functions
• 2.3.5 Understand that velocity and acceleration are rates of change
• 2.3.6 Know the difference between velocity and speed
• 2.3.7 Use appropriate units of measurement when giving numeric answers to position, velocity, and acceleration problems

Terminology

Terms you should be able to define: average velocity, instantaneous velocity, position function, velocity, acceleration, speed, height function

Text Notes

Some texts include other applications of derivative at this point such as business and economics. Since this is a STEM based Calculus course we will primarily focus on the engineering applications.

Mini-Lectures and Examples

STUDY: Derivatives and Motion

Supplemental Resources (optional)

Geogebra Exploration: Average and Instantateous Rate of Change, Mark Renault

rev. 2020-10-10