## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson

# Chapter 6 - Dynamics I: Motion Along a Line - Exercises and Problems - Page 155: 37

#### Answer

The velocity at t = 4 seconds is $4.5 ~m/s$.

#### Work Step by Step

From the graph, we can see that the average force from 0 to 3 seconds is 3.0 N. We can use the average force to find the average acceleration from 0 to 3 seconds; $F_{ave} = m~a_{ave}$ $a_{ave} = \frac{F_{ave}}{m}$ $a_{ave} = \frac{3.0~N}{2.0~kg}$ $a_{ave} = 1.5~m/s^2$ We can find the velocity at t = 3 seconds; $v_f = v_0+a_{ave}~t$ $v_f = 0+(1.5~m/s^2)(3~s)$ $v_f = 4.5~m/s$ Since the force from t = 3 s to t = 4 s is zero, the acceleration is also zero. Therefore, the velocity at t = 4 s is equal to the velocity at t = 3 s. The velocity at t = 4 seconds is $4.5 ~m/s$.

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