Equal-mass fragmentation energy budget ($\Delta K=\frac{1}{2}m{w}^2$)

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 $m{w}^2/2$, 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.