A box of mass \( m \) is initially at rest on a horizontal surface. A constant horizontal force ...

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A box of mass \( m \) is initially at rest on a horizontal surface. A constant horizontal force of \( m g / 2 \) is applied to the box directed to the right. The coefficient of friction of the surface changes with the distance pushed as \( \mu=\mu_{0} x \) where \( x \) is the distance from the initial location. For what distance is the box pushed until it comes to rest again
(a) \( \frac{2}{\mu_{0}} \)
(b) \( \frac{1}{\mu_{0}} \)
(c) \( \frac{1}{2 \mu_{0}} \)
(d) \( \frac{1}{4 \mu_{0}} \)
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