Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 2 - Motion Along a Straight Line - Problems: 20c

Answer

For positive $t$ values.

Work Step by Step

Acceleration is defined as $$a=\frac{d^2}{dt^2}(x(t))=x''(t)$$ Taking the first derivative of position yields $v(t)=20-15t^2$. Taking the derivative of velocity yields an acceleration of $$a(t)=-30t$$ In this equation, if $t$ is positive, acceleration is negative, since a negative times a positive is a negative.
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