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Calculus / Calculus: Early Transcendentals 9 / Chapter 6.4 / Problem 34

Calculus: Early Transcendentals | 9th Edition | ISBN: 9781337613927 | Authors: Daniel K. Clegg, Saleem Watson, James Stewart

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?When a particle is located a distance \(x\) meters from the origin, a force of \(\cos

Chapter 5, Problem 34

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QUESTION:

When a particle is located a distance \(x\) meters from the origin, a force of \(\cos (\pi x / 3)\)newtons acts on it. How much work is done in moving the particle from \(x=1\) to \(x=2 ?\) Interpret your answer by considering the work done from \(x=1\) to \(x=1.5\) and from \(x=1.5\) to \(x=2\).

Equation Transcription:

$x$

$cos(\pi{}x/3)$

$x=1\$

$x=2?$

$x=1$

$x=1.5$

$x=1.5$

$x=2$

Text Transcription:

x

cos(pi x/3)

x=1

x=2?

x=1

x=1.5

x=1.5

x=2

Questions & Answers

QUESTION:

When a particle is located a distance \(x\) meters from the origin, a force of \(\cos (\pi x / 3)\)newtons acts on it. How much work is done in moving the particle from \(x=1\) to \(x=2 ?\) Interpret your answer by considering the work done from \(x=1\) to \(x=1.5\) and from \(x=1.5\) to \(x=2\).

Equation Transcription:

$x$

$cos(\pi{}x/3)$

$x=1\$

$x=2?$

$x=1$

$x=1.5$

$x=1.5$

$x=2$

Text Transcription:

x

cos(pi x/3)

x=1

x=2?

x=1

x=1.5

x=1.5

x=2

ANSWER:

Step 1 of 3

In the given case and

Therefore

First, let us evaluate

We will substitute

On differentiating, we get

Substitute back , to get

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