I'm Given:
At one instant, the center of mass of a system of two particles is located on the x-axis at x = 2.0 m and has a velocity of (5.0 m/s) \hat I. One of the particles is at the origin. The other particle has a mass of 0.10 kg and is at rest on the x-axis at x = 8.0 m

What is the formula I would need to use to find the mass at the particle at the origin?

The center of mass is determined by locating the point where the masses times the distance to the center of mass sum to zero. In this case you have only two masses.



It seems to me that the velocity is irrelevant, but someone correct me if I'm wrong. The center of mass will change with time since one of the particles is moving. Maybe this is another part of the problem.

would your M1 = .1 D1 = 8.0 and your M2 = ? And D2 = 0

No. The masses are correct, but the distances are not. The distances are the distances from the center of gravity to their locations. The center of mass is at x=+2. Therefore, the mass at the "origin" is at -2 units from the center of gravity. The other mass is at +6 units from the center of gravity (think about it -- draw a line and plot the positions on the line).