Explanation Calculation: Consider the given position vector of a particle, r = t − t 2 i − t 2 j . Differentiate the position vector to find the velocity as, v t = d d t t − t 2 i − d d t t 2 j = 1 − 2 t i − 2 t j Differentiate the speed given by d s d t = v t . v t = 1 − 2 t 2 + − 2 t 2 = 4 t 2 + 1 − 4 t + 4 t 2 = 8 t 2 − 4 t + 1 Consider the above equation. v t = 8 t 2 − 4 t + 1 â€¦â€¦ (1) To find the critical points, differentiate equation (1). d d t v t = d d t 8 t 2 − 4 t + 1 1 2 = 1 2 8 t 2 − 4 t + 1 1 2 − 1 d d t 8 t 2 − 4 t + 1 = 1 2 8 t 2 − 4 t + 1 − 1 2 16 t − 4 = 1 2 1 8 t 2 − 4 t + 1 16 t − 4 For the critical points, substitute d d t v t = 0 . 1 2 1 8 t 2 − 4 t + 1 16 t − 4 = 0 16 t − 4 = 0 16 t = 4 t = 1 4 Hence, the critical point is t = 1 4

Calculus Early Transcendentals, Binder Ready Version

11th Edition

ISBN: 9781118883822

Author: Howard Anton, Irl C. Bivens, Stephen Davis

Publisher: WILEY

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Question

Chapter 12.6, Problem 14ES

To determine

To calculate: The value of the minimum speed of the particle and its location if the motion of a particle is described by the position vector, r=t−t2i−t2j .

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Chapter 12.6, Problem 13ES

Chapter 12.6, Problem 15ES

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Chapter 12 Solutions

Calculus Early Transcendentals, Binder Ready Version

Ch. 12.1 - Prob. 1QCE Ch. 12.1 - Describe the graph of rt=1+2t,1+3t.Ch. 12.1 - Prob. 3QCE Ch. 12.1 - Prob. 4QCE Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Prob. 5ES Ch. 12.1 - Prob. 6ES

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The value of the minimum speed of the particle and its location if the motion of a particle is described by the position vector , r = t − t 2 i − t 2 j .

Solution Summary: The author calculates the minimum speed of the particle and its location if the motion of a particle is described by the position vector.

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To calculate: The value of the minimum speed of the particle and its location if the motion of a particle is described by the position vector, r=t−t2i−t2j .

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Chapter 12 Solutions