A metro train leaves a station from rest and speeds up at 1.2 m/s² for 15 s…

Step 1. Cruising speed. $v = 1.2\ \text{m/s}^2 \times 15\ \text{s} = 18\ \text{m/s}$.

Step 2. Braking time. $\dfrac{18\ \text{m/s}}{1.5\ \text{m/s}^2} = 12\ \text{s}$.

Step 3. Areas. $\tfrac12 (15\ \text{s})(18\ \text{m/s}) = 135\ \text{m}$, $50\ \text{s} \times 18\ \text{m/s} = 900\ \text{m}$, $\tfrac12 (12\ \text{s})(18\ \text{m/s}) = 108\ \text{m}$. In all, $1143\ \text{m}$.

Step 4. Time and average. $15\ \text{s} + 50\ \text{s} + 12\ \text{s} = 77\ \text{s}$, so $\dfrac{1143\ \text{m}}{77\ \text{s}} = 14.8\ \text{m/s}$.