= Equal-mass fragmentation energy budget
{title2=$\Delta K=\tfrac12mw^2$}
If a mass m moving at u splits into equal fragments at velocities $u\pm w$, <conservation of momentum> fixes their centre-of-mass velocity. Their kinetic energy increases by $mw^2/2$, independent of u. Thus an internal release energy Q gives $w=\sqrt{2Q/m}$. A front fragment must exceed a leading target's speed to close a pre-existing separation; merely matching speed does not intercept it. This kinematic result does not specify subsequent capture or braking.
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