Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 12 - Kinematics of a Particle - Section 12.3 - Rectilinear Kinematics: Erratic Motion - Problems - Page 29: 46

Answer

At $s=75$ ft, $v=27.4$ ft /s At $s=100$ ft, $v=37.4$ ft/s

Work Step by Step

$0\leq s < 100 $ $\int_0^v v dv = \int_0^s 5 ds$ $\frac{1}{2}v^2=5$ s $v=\sqrt{10s}$ At $s=75$ ft, $v=\sqrt{750}=27.4$ ft /s $v dv = a ds$ $\int_{31.623}^v v dv = \int_{100}^{125} [5 + 6(\sqrt{s} - 10)^\frac{5}{3}]ds$ $\frac{1}{2}v^2|^v_{31.623}=201.0324$ $v=37.4$ ft/s
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