Chapter 13, Problem 16RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

The figure shows the curve *C* traced by a particle with position vector **r**(*t*) at time *t*.

(a) Draw a vector that represents the average velocity of the particle over the time interval 3â‰¤ *t* â‰¤ 3.2.

(b) Write an expression for the velocity **v**(3).

(c) Write an expression for the unit tangent vector **T**(3) and draw it.

**(a)**

To determine

**To draw:** A vector that represents the average velocity of the particle over the time interval

Explanation

**Given data:**

The figure shows the curve *C* traced by the particle with position vector *t*.

The interval of the time is given as

**Formula used:**

The expression to find the average velocity of the particle over the time interval

**Calculation:**

Calculation of average velocity vector is as follows.

Substitute 3.2 for *b* and 3 for *a* in equation (1),

Therefore, the average velocity vector of the particle over the time interval

**(b)**

To determine

**To find:** The expression for the velocity

**(c)**

To determine

**To write:** The expression for the unit tangent vector

Sect-13.1 P-1ESect-13.1 P-2ESect-13.1 P-3ESect-13.1 P-4ESect-13.1 P-5ESect-13.1 P-6ESect-13.1 P-7ESect-13.1 P-8ESect-13.1 P-9ESect-13.1 P-10E

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