Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 13 - Section 13.1 - The Indefinite Integral - Exercises - Page 961: 86

Answer

Fill the blanks with: velocity,$\qquad$ acceleration

Work Step by Step

We defined velocity as the derivative of position. If s $=s(t)$ is the position of an object at time $t$, then its velocity is given by the derivative $v=\displaystyle \frac{ds}{dt}$. So, position (=distance, if direction doesn't change) is an antiderivative of velocity. We also defined $a=\displaystyle \frac{dv}{dt}$: acceleration is the derivative of velocity. So, velocity is an antiderivative of acceleration.
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