Explanation r ( t ) = location of the particle. v ( t ) = d r d t = velocity of the particle. Given: Path of the particle is d r d t = 〈 2 t − 1 / 2 , 6 , 8 t 〉 -------------(1) r ( 1 ) = 〈 4 , 9 , 2 〉 --------------------(2) Calculation: To find out the location of the particle we integrate equation (1) with respect to t as r ( t ) = 〈 ∫ 2 t − 1 / 2 d t + a , ∫ 6 d t + b , ∫ 8 t d t + c 〉 Where a, b and c are the integration constants yet to determined, the above equation reduced to r ( t ) = 〈 4 t 1 / 2 + a , 6 t + b , 4 t 2 + c 〉 ---------------------(3) From equation (2), we are given that r ( 1 ) = 〈 4 + a , 6 + b , 4 + c 〉 = 〈 4 , 9 , 2 〉 On equating we get, 4 + a = 4 6 + b = 9 4 +

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 14.2, Problem 58E

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(a) Location of a particle at $t = 4$ .

(b) Velocity of a particle at $t = 4$ .

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Chapter 14.2, Problem 57E

Chapter 14.2, Problem 59E

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Chapter 14 Solutions

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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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(a) Location of a particle at t = 4 . (b) Velocity of a particle at t = 4 .

Solution Summary: The author explains how to calculate the velocity of a particle at t = 4 and the location of the particle.

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(a) Location of a particle at $t = 4$ .

(b) Velocity of a particle at $t = 4$ .

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Chapter 14 Solutions

(a) Location of a particle at t = 4 . (b) Velocity of a particle at t = 4 .

Solution Summary: The author explains how to calculate the velocity of a particle at t = 4 and the location of the particle.

Concept explainers

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(a) Location of a particle at t=4. (b) Velocity of a particle at t=4.

Want to see the full answer?

Chapter 14 Solutions

(a) Location of a particle at $t = 4$ .

(b) Velocity of a particle at $t = 4$ .