Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 4 - Dynamics: Newton's Laws of Motion - Problems - Page 103: 44

Answer

The initial speed of the car was 34 m/s.

Work Step by Step

The force of kinetic friction acted against the car's motion to bring the car to a stop. Let's calculate the magnitude of the acceleration caused by the force of kinetic friction. $ma = F_f$ $ma = mg~\mu_k$ $a = g ~\mu_k$ $a = (9.8 ~m/s^2)(0.80)$ $a = 7.8 ~m/s^2$ The magnitude of acceleration is $7.8 ~m/s^2$. Because the car was decelerating, the acceleration is $-7.8 ~m/s^2$. $v^2 - v_0^2 = 2ax$ $0 - v_0^2 = 2(-7.8 ~m/s^2)(72 ~m)$ $v_0 = \sqrt{(2)(7.8 ~m/s^2)(72 ~m)}$ $v_0 = 34 ~m/s$ The initial speed of the car was therefore 34 m/s.
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