what is the translational motion with the velocity of the center of mass?

and that is the internal motion relative to the center of mass? could give me some examples? desire to relate since I need to find out what is the kinetic energy in the center-of-mass of two particles, one moving and one stationary. Note: they collide

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The center of mass of a two-particle system is, by definition, at position

$$x_\textrm{com} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}.$$

The relative position of your particles relative to the CoM can be found by substracting the position of the CoM:

$$x'_1 = x_1 - x_\textrm{com},\ x'_2 = x_2 - x_\textrm{com}.$$

That should help you get started. Try differentiating those expressions to come up with how velocities relate, and what the kinetic energy would be.

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