Explanation Given Info : Acceleration a ( t ) = cos t k Initial velocity v ( 0 ) = 1 i − 1 j Initial position r ( 0 ) = 1 i Formula Used: (i) Apply the formula for velocity vector v ( t ) = ∫ a ( t ) d t + C 1 (iii) Apply the formula for position vector r ( t ) = ∫ v ( t ) d t + C 2 Here, all alphabets are in their usual meanings. Calculation: Apply the formula for velocity v ( t ) = ∫ a ( t ) d t + C 1 v ( t ) = ∫ cos t k d t + C 1 v ( t ) = − sin t k + C 1 − − − − − ( i ) Now, we shall apply given condition for initial velocity vector in equation (i) to calculated the integral constant ‘C 1 ’ 1 i − 1 j + 0 k = v ( 0 ) = 0 i + 0 j + 0 k + C 1 o r , C 1 = 1 i − 1 j − − − − − − ( i i ) From equation (i) and (ii), the required expression for velocity vector v ( t ) can be calculated as v ( t ) = − sin t k + ( 1 i − 1 j ) v ( t ) = 1 i − 1 j − sin t k − − − − ( a ) v ( t ) = ( 1 , − 1 , − sin t ) Apply the formula for position vector r ( t ) = ∫ v

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.5, Problem 18E

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To calculate position vector $r (t)$ and velocity $v (t)$ from the given conditions.

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Chapter 14.5, Problem 17E

Chapter 14.5, Problem 19E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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To calculate position vector r ( t ) and velocity v ( t ) from the given conditions.

Solution Summary: The author explains how to calculate position vector r ( t ) and velocity v from the given conditions.

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To calculate position vector $r (t)$ and velocity $v (t)$ from the given conditions.

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Chapter 14 Solutions

To calculate position vector r ( t ) and velocity v ( t ) from the given conditions.

Solution Summary: The author explains how to calculate position vector r ( t ) and velocity v from the given conditions.

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To calculate position vector r(t) and velocity v(t) from the given conditions.

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Chapter 14 Solutions

To calculate position vector $r (t)$ and velocity $v (t)$ from the given conditions.