The Work Done on a Sliding Box: How to Calculate Friction and Applied Force

[murrskeez]

Homework Statement

A box of mass m is sliding along a horizontal surface.
Part A) The box leaves position x=0 with a speed v₀. The box is slowed by a constant frictional force until it comes to rest at a position x=x₁. Find F_f, the magnitude of the average frictional force that acts on the box. (express in terms of m, v₀, and x₁.
I found the correct answer to part A...(F_f=(mv₀²)/2x₁)

Part B) After the box comes to rest at a position x₁, a person starts pushing the box giving it a speed v₁. When the box reaches position x₂ (where x₂>x₁), how much work W_p has the person done on the box? Assume that the box reaches x₂ after a person has accelerated it from rest to speed v₁. Express the work in terms of m,v₀,x₁,x₂, and v₁.

Homework Equations

W=ΔKE
W=F*d

The Attempt at a Solution

So I figured that the total work would be the work done in part A (-(mv₀²)/2x₁)*(x₁)
added to the work done between x₁ and x₂:
-(mv₀²(x₂-x₁))/2x₁

however when I add these two solutions, it tells me that the answer needs to include v₁. So then I thought to solve for v₁ by setting the work done between x₁ and x₂ equal to the change in kinetic energy between that time frame which gave me:

KE = (mv₁²)/2 = work between x₁ and x₂

v₀²=(x₁v₁²)/-(x₂-x₁)

so that allowed me to have v₁ in my final answer...but mastering physics is still telling me it's incorrect.

Any advice/help would be great.

 

[Simon Bridge]

You were nearly right the first time - what distance does the friction force act over?