The symbol represents time For problems from the Text – Principles of Dynamics – D. Greenwood, the numbers areindicated in bold.Q1. A particle follows a planar path defined by x=(A/kC)sin(kç), y = (A/kC)cos(kG),such that its speed is v = B5 , where A, k and B are constants. Determine the velocityand acceleration at 5 = 47/3k.

r(ζ)=xi^+yj^r(ζ)=(A/ζ)sin(κζ)i^+(A/ζ)cos(κζ)j^taking derivative of…

Answered: For problems from the Text - Principles…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The symbol represents time

For problems from the Text – Principles of Dynamics – D. Greenwood, the numbers are
indicated in bold.
Q1. A particle follows a planar path defined by x=(A/kC)sin(kç), y = (A/kC)cos(kG),
such that its speed is v = B5 , where A, k and B are constants. Determine the velocity
and acceleration at 5 = 47/3k.

Expert Solution

Step 1

$r (ζ) = x \hat{i} + y \hat{j} r (ζ) = (A / ζ) \sin (κ ζ) \hat{i} + (A / ζ) \cos (κ ζ) \hat{j} t a k i n g d e r i v a t i v e o f r (ζ) v (ζ) = \frac{d r (ζ)}{d ζ} = (k A / ζ) \cos (κ ζ) \hat{i} - (k A / ζ) \sin (κ ζ) \hat{j} a t ζ = 4 π / 3 k v (ζ) = \frac{k^{2} A}{4 π / 3} \cos (4 π / 3) - \frac{k^{2} A}{4 π / 3} \cos (4 π / 3) = - \frac{k^{2} A}{4 π / 3} [0.5 \hat{i} + 0.866 \hat{j}] m / s^{2}$

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