College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 1 - Section 1.6 - Dimensional Analysis - Practice Problem - Page 12: 1.9


The kinetic energy increases by 56%

Work Step by Step

Kinetic energy has units of $kg~m^2~s^{-2}$ Velocity has units of $m~s^{-1}$ Therefore, we need to square the velocity to find the kinetic energy. We also need to include mass $m$ since kinetic energy includes units of $kg$. Then $KE = C~m~v^2$, where $C$ is some constant. $\frac{KE'}{KE} = \frac{C~m~(v')^2}{C~m~v^2} = \frac{(1.25v)^2}{v^2} = 1.56$ The kinetic energy increases by 56%.
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