## Thomas' Calculus 13th Edition

Published by Pearson

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

#### Answer

$k=\dfrac{1}{5}$

#### 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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