Gravitational attraction question

[physninj]

Homework Statement

two point masses (400 kg) are 10^14 m apart in deep space under no gravitational attraction besides each others. find their velocity when they are 1000 m apart.

Homework Equations

-G (m_1m_2)/r^2=F

The Attempt at a Solution

I integrated the equation above plugging in the 400 kg for m1 and m2 from 10^14 to 1000. I believe this gave me the work required to bring one of them to that distance so i set it equal to ΔKE. This became (1/2)mv_f^2 because they start from rest. Now my question is whether that mass is 400 kg or 800 kg or if I'm on the right track. I just put one of the mass in that then solved and got 7.3226*10^-6. And I think that is the velocity of each of the masses. Anybody care to disagree? Thank you.

 

[Doc Al]

As they come together, their mutual gravitational PE is transformed into the kinetic energy of both masses.