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: 22

Answer

Velocity vector $v(t)$ and acceleration vector $a(t)$ are orthogonal.

Work Step by Step

Tangential acceleration $a_T$ is zero because the particle moves with same speed. Let us consider $v(t)$ as velocity vector and $a(t)$ represents as acceleration vector. Use formula $a_T=\dfrac{v(t) \cdot v'(t)}{|v(t)|}$ When $a_T=0$ $\implies$ $v(t) \cdot v'(t)=0$ Hence, we can see that $v(t)$ is perpendicular to $v'(t)$ or, the terms velocity vector $v(t)$ and acceleration vector $a(t)$ are orthogonal.
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