Chapter 13, Problem 17RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

A particle moves with position function **r**(*t*) = *t* ln *t* **i** + *t* **j** + *e*^{−t} **k**. Find the velocity, speed, and acceleration of the particle.

To determine

**To find:** The velocity of a particle that moves with the position function

Explanation

**Given data:**

The particle moves with the position function

**Formula used:**

Write the expression to find the velocity with the position function

Write the required differentiation formulae to obtain the solution as follows.

Write the expression to find the speed of a particle with the position function

Here,

Write the expression to find the acceleration of a particle with the position function

Substitute

Simplify the expression as follows.

Thus, the velocity of a particle that moves with the position function

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