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


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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.