Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 50

Answer

$$ 20\ \ m/s,\ \ \ -34.64 \mathrm{cm} / \mathrm{s}^{2}$$

Work Step by Step

Given $$s(t) = 300 + 40 \sin t $$ The velocity is given by \begin{align*} s'(t)&= 40\cos t\\ s'(\pi/3)&= 20\ \ m/s \end{align*} and the acceleration is given by \begin{align*} s''(t)&= -40\sin t\\ s''(\pi/3)&= -34.64 \mathrm{cm} / \mathrm{s}^{2} \end{align*}
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