Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 14 - Calculus of Vector-Valued Functions - 14.3 Arc Length and Speed - Preliminary Questions - Page 725: 3


(a) 4 (b) No

Work Step by Step

(a) The rate of change of $L(t)$ is $v(t)$, and $v(2)=2^2=4$. (b) $L(t)$ is defined to be the total distance traveled, which is only equal to displacement when the path is a line. The problem states that the path is a parabola, so the distance traveled is greater than the displacement from the origin.
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