The position function of a particle is given by r(t) = (t2, 2t, t2 - 16t). When is the speed a minimum? Step 1 To find when the speed is a minimum, we need to find the speed as a function of t, then find its derivative and see when it is 0. We begin by finding the velocity vector. Since r(t) = (t2, 2t, t² - 16t), we have v(t) = r(t) = [21, 2, 21-16] (2t, 2, 2t - 16) Step 2 We remember that the speed is the magnitude of the velocity vector, and is calculated as follows. |v(t)=√(2t)² + (2)² + (2t - 16)² = √ t +

The position function of a particle is given by r(t) = (t2, 2t, t2 - 16t). When is the speed a minimum? Step 1 To find when the speed is a minimum, we need to find the speed as a function of t, then find its derivative and see when it is 0. We begin by finding the velocity vector. Since r(t) = (t2, 2t, t² - 16t), we have v(t) = r(t) = [21, 2, 21-16] (2t, 2, 2t - 16) Step 2 We remember that the speed is the magnitude of the velocity vector, and is calculated as follows. |v(t)=√(2t)² + (2)² + (2t - 16)² = √ t +

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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