Apply Momentum Conservation to Collisions Practice Test

Two carts collide head-on on a frictionless track. Cart A has mass $m_A=1.0\ \text{kg}$ and initial velocity $v_{A i}=+8.0\ \text{m/s}$ (right). Cart B has mass $m_B=3.0\ \text{kg}$ and initial velocity $v_{B i}=-2.0\ \text{m/s}$ (left). The collision is perfectly inelastic (they stick together). Taking rightward as positive, what is the common final velocity $v_f$?

Two carts collide on a low-friction track. Cart 1 has mass $m_1 = 1.5,\text{kg}$ and initial velocity $v_{1 i} = +8.0,\text{m/s}$ (right). Cart 2 has mass $m_2 = 3.0,\text{kg}$ and is initially at rest ($v_{2 i} = 0$). After an inelastic collision (they bounce apart), Cart 1 moves left at $v_{1 f} = -2.0,\text{m/s}$. Taking rightward as positive, what is Cart 2's final velocity $v_{2 f}$ (in m/s)?