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## Homework Statement

A block of mass [itex]m[/itex] is at rest at the origin at [itex]t=0[/itex]. It is pushed with constant force [itex]F_0[/itex] from [itex]x=0[/itex] to [itex]x=L[/itex] across a horizontal surface whose coefficient of kinetic friction is [itex]\mu_k=\mu_0(1-x/L)[/itex]. That is, the coefficient of friction decreases from [itex]\mu_0[/itex] at [itex]x=0[/itex] to zero at [itex]x=L[/itex].

Find an expression for the block's speed as it reaches position [itex]L[/itex].

## The Attempt at a Solution

I ended up with [itex]F_{net}=F_0 - mg\mu_0 + \frac{mgx}{L}[/itex]

I can use this to find [itex]a[/itex] in terms of [itex]x[/itex], but I don't know what use that would be.