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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Finding Velocity and Acceleration Along a Plane Curve In Exercises 3-10, the position vector r describes the path of an object moving in the x y-plane.

(a) Find the velocity vector, speed, and acceleration vector of the object.

(b) Evaluate the velocity vector and acceleration vector of the object at the given point.

(c) Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point.

Position Vector Point

**(a)**

To determine

The velocity vector, speed and acceleration vector of the object for a provided position vector r → ( t ) = 〈 t − sin t , 1 - cos t 〉 and at a given point ( π , 2 ) .

Explanation

**Given:**

The given vector and point is

**Explanation:**

Consider the provided position vector is:

Derivative of the position vector gives velocity vector:

**(b)**

To determine

The velocity vector and acceleration vector at the given point ( π , 2 )

**(c)**

To determine

The sketch a graph and the velocity and acceleration vector at the given point.

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

Single Variable Calculus: Early Transcendentals, Volume I

Applied Calculus

Multivariable Calculus

Calculus: An Applied Approach (MindTap Course List)

Calculus: Early Transcendentals

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendental Functions

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)

Statistics for The Behavioral Sciences (MindTap Course List)

Understanding Basic Statistics

Single Variable Calculus

Mathematical Excursions (MindTap Course List)

Mathematical Applications for the Management, Life, and Social Sciences

Finite Mathematics

Intermediate Algebra

Probability and Statistics for Engineering and the Sciences

Single Variable Calculus: Early Transcendentals

Elementary Technical Mathematics

Contemporary Mathematics for Business & Consumers

Elementary Geometry For College Students, 7e

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Calculus of a Single Variable

Calculus: Early Transcendental Functions (MindTap Course List)

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences