**Part A**

Work-energy theorem:

$\overline{){\mathbf{W}}{\mathbf{=}}{\mathbf{\u2206}}{\mathbf{K}}}$

A box of mass m is sliding along a horizontal surface.

Part A. The box leaves position x = 0 with speed v_{0}. The box is slowed by a constant frictional force until it comes to rest at position x = x_{1}. Find F_{t}, the magnitude of the average frictional force that acts on the box (Since you don't know the coefficient of friction, don't include it in your answer) Express the frictional force in terms of m, v_{0} and x_{1}.

Part B. After the box comes to rest at position x_{1} a person starts pushing the box, giving a speed v_{1}. When the box reaches position x_{2} (where x_{2} > x_{1}), how much work W_{P} has the person done on the box? Assume that the box reaches x_{2} after the person has accelerated it from rest to speed v_{1}. Express the work in terms of m, v_{0}, x_{1}, x_{2}, and v_{1}.

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