Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 13 - Section 13.4 - Motion in Space: Velocity and Acceleration - 13.4 Exercise - Page 878: 11


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

Work Step by Step

Given: $r(t)=\sqrt 2 ti+e^tj+e^{-t}k$ Our aim is to calculate the velocity vector, acceleration vector and speed. In order to calculate the all above terms we will use formulas, such as: $v(t)=r'(t)$ and $a(t)=v'(t)$ and speed is the magnitude of the velocity vector, that is $s(t)=|v(t)|$. Now, $v(t)=r'(t)=\sqrt 2 i+e^tj-e^{-t}k$ $a(t)=v'(t)=e^t j+e^{-t}k$ $s(t)=|v(t)|=\sqrt {(\sqrt 2)^2+(e^t)^2+(-e^{-t})^2}=e^t+e^{-t}$ Hence, the required answers are: $\sqrt 2 i+e^tj-e^{-t}k$, $e^t j+e^{-t}k$ , $e^t+e^{-t}$
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