Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 13: Vector-Valued Functions and Motion in Space - Practice Exercises - Page 777: 5



Work Step by Step

The vector formula for curvature can be found as: $k=\dfrac{|v \times a(t)|}{|v^3|}$ and $v \times a(t)=25 \ k$ $\implies |v \times a(t)|=25 $ Next, $|v|=\sqrt {(3)^2+(4)^2}=5$ Therefore, $k=\dfrac{|v \times a(t)|}{|v^3|}=\dfrac{25}{(5)^3}=\dfrac{1}{5}$
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