Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 13 - Vector Functions - 13.4 Motion in Space: Velocity and Acceleration - 13.4 Exercises - Page 918: 11


$\sqrt 2 i+e^tj-e^{-t}k$, $e^t j+e^{-t}k$ , $e^t+e^{-t}$

Work Step by Step

As we are given $r(t)=\sqrt 2 ti+e^tj+e^{-t}k$ Need to determine velocity vector, acceleration vector and speed. We have $v(t)=r'(t)$ and $a(t)=v'(t)$ and speed is the magnitude of the velocity vector, that is $s(t)=|v(t)|$. $v(t)=r'(t)=\sqrt 2 i+e^tj-e^{-t}k$ [ given: $r(t)=\sqrt 2 ti+e^tj+e^{-t}k$] Also, $a(t)=v'(t)=e^t j+e^{-t}k$ Now, $s(t)=|v(t)|=\sqrt {(\sqrt 2)^2+(e^t)^2+(-e^{-t})^2}=e^t+e^{-t}$
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