In a closed system, two objects collide elastically. Object A with a mass of 2 kg moving at 3 m/s collides with object B, which has a mass of 4 kg and is initially at rest. What is the final velocity of object A after the collision if momentum is conserved?

The initial momentum is \(2\,\text{kg}\times3\,\text{m/s}=6\,\text{kg·m/s}\). Because the collision is elastic, both momentum and kinetic energy are conserved, giving the formula for the first object's final speed: \(v_{1f}=\frac{m_1-m_2}{m_1+m_2}\,v_{1i}+\frac{2m_2}{m_1+m_2}\,v_{2i}\). Substituting \(m_1=2\text{ kg}, m_2=4\text{ kg}, v_{1i}=3\text{ m/s}, v_{2i}=0\) yields \(v_{1f}=\frac{2-4}{6}\times3=-1\text{ m/s}\). Thus after the collision object A moves backward at \(1\text{ m/s}\) (opposite its initial direction). A quick check: the final momentum \(2(-1)+4(2)=6\) kg·m/s, matching the initial momentum.