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: 18b

Answer

velocity = 48m/s

Work Step by Step

The position is given by $ x = 12t^2 - 2t^3 $ Since the velocity equation is the derivative of the position equation we need to find $\frac{d}{dt} (12t^2 - 2t^3) $ Since $\frac{d}{dt} t^n = n*t^(n-1)$ then $\frac{d}{dt} (12t^2 - 2t^3) = 12(2)t - 2(3)t^2 = 24t - 6t^2 $ To find the velocity at t =3, we need to plug this into the velocity equation This gives us $ 24(3) - 6(2)^2 = 72 - 24 = 48m/s$
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