Elastic head-on collision velocities (Elastic 1D: v1f and v2f from m1,m2,u1,u2)

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Elastic 1D: v1f and v2f from m1,m2,u1,u2

What each symbol means

SymbolWhat it stands for
m_1,m_2Masses (kg)
u_1,u_2Initial velocities along line (m/s)
v_{1f},v_{2f}Final velocities (m/s)

When to use this

Smooth spheres/lines; elastic (e=1); no external impulse during collision; same sign convention for all velocities.