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 - General Problems - Page 107: 88

Answer

The motorcyclist will emerge from the sandy stretch with a speed of 14 m/s.

Work Step by Step

We can use a force equation to find the acceleration. $ma = F_f$ $ma = mg ~\mu$ $a = g ~\mu = (9.80 ~m/s^2)(0.70) = 6.86 ~m/s^2$ The can use this rate of deceleration to find the speed after 15 meters: $v^2 = v_0^2 + 2ax$ $v = \sqrt{v_0^2 + 2ax}$ $v = \sqrt{(20.0 ~m/s)^2 - (2)(6.86 ~m/s^2)(15 ~m)}$ $v = 14 ~m/s$ The motorcyclist will emerge from the sandy stretch with a speed of 14 m/s.
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