Animate[Manipulate[
  Graphics[{{Red, 
     Disk[{If[t < (M^(0.5) + m^(0.5) - 5)/(v - u), v t, 
        v ((M^(0.5) + m^(0.5) - 5)/(v - 
              u)) + (t - ((M^(0.5) + m^(0.5) - 5)/(v - u))) (v M + 
             2 u m - v m)/(M + m)], 0}, M^(1/2)]}, {Green, 
     Disk[{If[
        t < (M^(0.5) + m^(0.5) - 5)/(v - u), -5 + u t, -5 + 
         v ((M^(0.5) + m^(0.5) - 5)/(v - 
              u)) + (t - ((M^(0.5) + m^(0.5) - 5)/(v - u))) (u M + 
             2 m m - u m)/(M + m)], 0}, m^(1/2)]}}, 
   PlotRange -> {{-10, 10}, {-5, 5}}], 
{{m, 1, "Mass of Green Disk"}, 1, 3}, 
{{M, 1, "Mass of Red Disk"}, 1, 3}, 
{{u, 1, "Velocity of Green Disk"}, 0, 5}, 
{{v, 0, "Velocity of Red Disk"}, -2, 2}], 
{{t, 0, "Press Play"}, 0, 20}, AnimationRunning -> False]