2 object gravitation, collision speed

AI Thread Summary
To determine the collision speed of two objects with mass m and radius r, initially at rest and a distance L apart, one must apply Newton's law of gravitation, Fg = G m^2/(r^2). The discussion emphasizes the need to formulate differential equations to describe the motion of the objects as they accelerate towards each other. A suggested approach involves using the relationship a = dv/dx * v to derive the necessary equations. The poster expresses uncertainty in writing these equations despite having solved a similar problem previously. Clarification on the formulation of the equations is sought to progress in finding the velocity at the moment of collision.
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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?
 
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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.
 

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