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Course: Calculus III
Topic: Vector-Valued Functions
Subtopic: Velocity and Acceleration

Overview

Vector valued functions describe the position of an object moving in space. Their first and second derivatives describe their velocity and acceleration.

Objectives

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

• 14.3.1 Given the vv function describing the position of an object in motion in 3D space, sketch the trajectory of the object and find it's velocity, speed, and acceleration
• 14.3.2 Understand straight line uniform (constant velocity) motion and circular motion
• 14.3.3 Integrate a vv function to find the velocity and position of an object moving in space given its acceleration
• 14.3.4 Analyze two-dimensional motion including range, time of flight, max height
• 14.3.5 Analyze three-dimensional motion and projectile motion

Terminology

Define: position, velocity, acceleration, uniform motion, circular motion, 2D motion, range of motion, time of flight, maximum height, 3D motion, projectile motion

Supplemental Resources (optional)

Dale Hoffman's Contemporary Calculus III: Dale Hoffman's Contemporary Calculus III: Derivatives & Antiderivatives of Vector-Valued Functions (study "Velocity" and "Acceleration" sections)

Paul's OL Notes - Calc III: Velocity and Acceleration

More tutorial videos if you need them are listed at James Sousa's MathIsPower4U - Calc II. Scroll down right column to "Vector Valued Functions". There are several related titles in the first half of that list.