Consider two particles of equal masses attached to each other by a light straight spring write the lagrangian center of mass

The lagrangian center of mass between two particles of equal mass can be calculated using the following equation: L=12MV2â’Uext.+Nâ‘i=112mi~v2iâ’Uint. M=â‘mi is the total mass, V is the speed of the center of mass, Uext.=â‘Uext.,i, and ~vi is the speed of the ith particle relative to the center of mass.

Speed is how fast you are going without direction specified
velocity is speed WITH a direction
acceleration is how quickly velocity is changing