Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 5 - Newton's Laws of Motion - Problems and Conceptual Exercises - Page 140: 6

Answer

$a=2.88 m/s^2, F=265N$

Work Step by Step

To find the force, use the formula $$F=ma$$ To find the acceleration, use a kinematics equation relating acceleration, initial velocity, final velocity, and distance. This is $$v_f^2=v_o^2+2a\Delta x$$ Solve for acceleration $a$ to get $$a=\frac{v_f^2-v_o^2}{2\Delta x}$$ Substitute known values of $v_o=0.0m/s$, $v_f=12m/s$, and $\Delta x=25m$ $$a=\frac{(12m/s)^2}{2(25m)}=2.88m/s^2$$ Substituting known values of $a=2.88m/s^2$ and $m=92kg$ yields a force of $$F=(92kg)(2.88m/s^2)=265N$$
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