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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

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Proof Prove that when an object is traveling at a constant speed, its velocity and acceleration vectors are orthogonal.

To determine

**To prove:** When an object is traveling at a constant speed, its velocity and acceleration vectors are orthogonal for the provided position vector

Explanation

**Given:**

The provided position vector is

**Formula used:**

The magnitude of the velocity vector gives speed:

**Proof:**

Consider the position vector,

Differentiate position vector with respect to *t* gives a velocity vector,

Differentiate velocity vector with respect to *t* gives an acceleration vector,

It is provided that speed is constant

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P-10PSCh-12 P-11PSCh-12 P-12PSCh-12 P-13PSCh-12 P-14PS

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Calculus: Early Transcendental Functions

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Single Variable Calculus: Early Transcendentals, Volume I

Applied Calculus

Calculus: Early Transcendentals

Calculus: An Applied Approach (MindTap Course List)

Finite Mathematics and Applied Calculus (MindTap Course List)

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Essentials Of Statistics

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Calculus (MindTap Course List)

Single Variable Calculus

Finite Mathematics

Understanding Basic Statistics

Statistics for The Behavioral Sciences (MindTap Course List)

Mathematical Applications for the Management, Life, and Social Sciences

Intermediate Algebra

Mathematical Excursions (MindTap Course List)

Probability and Statistics for Engineering and the Sciences

Single Variable Calculus: Early Transcendentals

Elements Of Modern Algebra

Elementary Technical Mathematics

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Contemporary Mathematics for Business & Consumers

Trigonometry (MindTap Course List)

Calculus of a Single Variable

Calculus: Early Transcendental Functions (MindTap Course List)

Finite Mathematics for the Managerial, Life, and Social Sciences

Elementary Geometry for College Students