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## Homework Statement

Find the velocity of v as a function of displacement x for a particle of mass m which starts from rest at x=0 and subject to the following force:

[tex]F=F_0+kv[/tex]

You could say mv = F0*t + kx, but the answer in the back of the book is an equation that is only in terms of x and v, not t. The answer in the back of the book involves ln.

## Homework Equations

Maybe this:

[tex]\ddot {x}= \frac{d \dot{x}}{dx}[/tex]

## The Attempt at a Solution

[tex]m\ddot{x}=F_0 +k\dot{x}[/tex]

[tex]m\dot{x} \frac{d\dot{x}}{dx}=F_0 +k\dot{x}[/tex]

[tex]m\dot{x} d\dot{x} = F_0dx + k\dot{x} dx[/tex]

[tex]\frac{1}{2}m\dot{x}^2 = F_0*x + ???[/tex]

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