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: 12


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

Work Step by Step

Given: $r(t)=t^2i+2t j+\ln t k$ 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, $v(t)=r'(t)=2ti+2+\frac{1}{t}k$ $a(t)=v'(t)=2i-\frac{1}{t^2}k$ $s(t)=|v(t)|=\sqrt {(2t)^2+(2)^2+(\frac{1}{t})^2}=2t+\frac{1}{t}$ Hence, the required answers are: $2ti+2+\dfrac{1}{t}k$, $2i-\dfrac{1}{t^2}k$ , $2t+\dfrac{1}{t}$
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