A trolley of mass 2.8 kg runs at 3.5 m/s into a trolley of mass 1.2 kg at rest…

Step 1. Common speed. $2.8\ \text{kg} \times 3.5\ \text{m/s} = (2.8\ \text{kg} + 1.2\ \text{kg})\,v$, so $v = \dfrac{9.8\ \text{kg m/s}}{4.0\ \text{kg}} = 2.45\ \text{m/s}$.

Step 2. Energy before. $\tfrac12 \times 2.8\ \text{kg} \times (3.5\ \text{m/s})^2 = 17.15\ \text{J}$.

Step 3. Energy after. $\tfrac12 \times 4.0\ \text{kg} \times (2.45\ \text{m/s})^2 = 12.0\ \text{J}$.

Step 4. Lost. $17.15\ \text{J} - 12.0\ \text{J} = 5.15\ \text{J}$.