Collision Lab

Coefficient of restitution:
  e = (v₂ − v₁) / (u₁ − u₂)

Closed-form 1-D collision:
  v₁ = ((m₁ − e·m₂)u₁ + (1+e)m₂·u₂) / (m₁+m₂)
  v₂ = ((m₂ − e·m₁)u₂ + (1+e)m₁·u₁) / (m₁+m₂)

Always: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Energy lost = ½ · m₁m₂/(m₁+m₂) · (1−e²)(u₁−u₂)²

Try this: Set e = 1. Momentum and KE both match exactly: that's elastic. Drop e to 0 and watch the balls stick (their velocities become equal): that's perfectly inelastic, with maximum KE loss. With m₁ = m₂, e = 1 they exchange velocities: the JEE-favourite cradle result.