In a conservation of momentum problem, a 0.5 kg piece moves right at 3 m/s after an explosion, while a 1.5 kg piece moves left. If initial total momentum was zero, what is the velocity of the 1.5 kg piece?

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Momentum is conserved in an isolated system, so the total momentum before and after the explosion must be the same. Since the initial total momentum is zero, the momenta of the two pieces after the explosion must cancel each other out. The 0.5 kg piece moving right at 3 m/s has momentum p = 0.5 × 3 = +1.5 kg·m/s. To balance this, the 1.5 kg piece must carry momentum −1.5 kg·m/s. Its velocity is v = p/m = (−1.5) / 1.5 = −1.0 m/s, where the negative sign indicates motion to the left. The 1.5 kg piece therefore moves left at 1.0 m/s.