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So, a is acceleration, F is a force Vo is V-subscript-0 (V0) and you want to solve for something unspecified, is this correct?
Your notation is confusing - do you mean bold-face to be a vector? In which case, how can you have a scalar equal a vector? Shouldn't acceleration also be a vector?
If all these can be taken in the x direction ... ditching the bold-face:[tex]ma = V_0\frac{a^2}{a^2+x^2}[/tex]... perhaps you want to find x as a function of time?
Then why not rearrange so all the powers of "a" are on the left and all the others are on the right, substitute a=d²x/dt² and solve the differential equation?
Don't you get a quadratic in "a"?
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