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: 13


$e^t[(\cos t -\sin t)i+(\sin t+\cos t) j+(t+1) k])$, $e^t[-2\sin t i+2\cos t j+(t+2) k])$, $e^t \sqrt {t^2+2t+3}$

Work Step by Step

As we are given that $r(t)=e^t(\cos t i+\sin t j+t k)$ Need to determine the 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 $s(t)=|v(t)|$. $v(t)=r'(t)=e^t[(\cos t -\sin t)i+(\sin t+\cos t) j+(t+1) k])$ [ given: $r(t)=e^t(\cos t i+\sin t j+t k)$] Also, $a(t)=v'(t)=e^t[-2\sin t i+2\cos t j+(t+2) k])$ Thus, $s(t)=|v(t)|=e^t \sqrt {t^2+2t+3}$
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