2 object gravitation, collision speed

[aalasso]

Homework Statement

2 objects each with mass, m, and radius, r, are unaffected by any other objects. They are the distance L apart. At time t=0 , both are at rest. From then on they accelerate towards each other.
Determine the speed of the planets at the moment of collision.

Homework Equations

From assignment: "Use a= dv/dx * v in order to solve the problem".
Newtons law of gravitation: Fg= G m^2/(r^2)

The Attempt at a Solution

Well I would think that I'm supposed to make 1 or 2 differential equations, which I can then solve specifically by x_0=0 .
My problem is writing the equations, can anyone help, please?

 

[Nabeshin]

I have solved a very similar problem, but am uncertain of the solution! I obtained a position-time equation, from which I could easily differentiate and find velocity... Umm refer to my post in general physics if you want to see that.