3.105: Velocity–time graph: find $T$ and final acceleration

The diagram shows the velocity–time graph for a particle. The particle starts from rest and moves with constant acceleration $2\,\mathrm{ms}^{-2}$ for the first $T$ seconds. It then moves with constant velocity until $t=4$, and finally decelerates uniformly to rest at $t=8$. The total distance travelled is $27\,\mathrm{m}$.