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: 12


$2ti+2j+\dfrac{1}{t}k$, $2i-\dfrac{1}{t^2}k$ , $2t+\dfrac{1}{t}$

Work Step by Step

As we are given that $r(t)=t^2i+2t j+\ln t k$ 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 $s(t)=|v(t)|$. $v(t)=r'(t)=2ti+2j+\frac{1}{t}k$ [ given : $r(t)=t^2i+2t j+\ln t k$] Now, $a(t)=v'(t)=2i-\frac{1}{t^2}k$ Thus, $s(t)=|v(t)|=\sqrt {(2t)^2+(2)^2+(\frac{1}{t})^2}=2t+\frac{1}{t}$
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