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 - 14.5 Motion in 3-Space - Exercises - Page 744: 3



Work Step by Step

Since $r(t)=\lt t^3, 1-t, 4t^2\gt$, then the velocity vector is given by $$r'(t)=\lt 3 t^2, -1, 8t\gt$$ and the acceleration vector is given by $$r''(t)=\lt 6 t, 0, 8\gt.$$ Moreover, the speed at $t=1$ is $$v(1)=\|r'(1)\|=\sqrt{9+1+64}=\sqrt{74}.$$
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.