Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 6 - Dynamics I: Motion Along a Line - Exercises and Problems: 26

Answer

The velocity at t = 6 seconds is $4 ~m/s$

Work Step by Step

From the graph, we can see that the average force from 0 to 4 seconds is 5.0 N. We can use the average force to find the average acceleration from 0 to 4 seconds. Therefore: $F_{ave} = ma_{ave}$ $a_{ave} = \frac{F_{ave}}{m}$ $a_{ave} = \frac{5.0~N}{5.0~kg}$ $a_{ave} = 1.0~m/s^2$ We can find the velocity at t = 4 seconds. $v_f = v_0+a_{ave}~t$ $v_f = 0+(1.0~m/s^2)(4~s)$ $v_f = 4~m/s$ Since the force from t = 4 s to t = 6 s is zero, the acceleration is also zero. Therefore, the velocity at t = 6 s is equal to the velocity at t = 4 s. The velocity at t = 6 seconds is $4 ~m/s$.
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