A train starts from rest at a station $A$ and travels in a straight line to station $B$, where it comes to rest.
The train moves with constant acceleration $0.025{\text{ }}m{\text{ }}{s^{ - 2}}$ for the first $600{\text{ }}s$, with constant speed for the next $2600{\text{ }}s$, and finally with constant deceleration $0.0375{\text{ }}m{\text{ }}{s^{ - 2}}$.
a) Find the total time taken for the train to travel from $A$ to $B$.
b) Sketch the velocity-time graph for the journey and find the distance $AB$.
c) The speed of the train $t$ seconds after leaving $A$ is $7.5{\text{ }}m{\text{ }}{s^{ - 1}}$. State the possible values of $t$.
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