A 3.0 kg ball moving at 5.0 m/s makes a head-on elastic collision with a 2.0 kg ball at rest…

Step 1. $v_1 = \dfrac{1.0\ \text{kg}}{5.0\ \text{kg}} \times 5.0\ \text{m/s} = 1.0\ \text{m/s}$, still forward.

Step 2. $v_2 = \dfrac{6.0\ \text{kg}}{5.0\ \text{kg}} \times 5.0\ \text{m/s} = 6.0\ \text{m/s}$.

Step 3. Check energy. Before: $\tfrac12 \times 3.0\ \text{kg} \times 25\ \text{m}^2/\text{s}^2 = 37.5\ \text{J}$. After: $\tfrac12 \times 3.0\ \text{kg} \times 1\ \text{m}^2/\text{s}^2 + \tfrac12 \times 2.0\ \text{kg} \times 36\ \text{m}^2/\text{s}^2 = 1.5\ \text{J} + 36\ \text{J} = 37.5\ \text{J}$.