A train moves along a straight horizontal track between two stations \(R\) and \(S\). Initially the train is at rest at \(R\). The train accelerates uniformly at \(\frac { 1 } { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) from rest at \(R\) until it is moving with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). For the next 200 seconds the train maintains a constant speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The train then decelerates uniformly at \(\frac { 1 } { 4 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it comes to rest at \(S\).
Find
the time taken by the train to travel from \(R\) to \(S\),
the distance from \(R\) to \(S\),
the average speed of the train during the journey from \(R\) to \(S\).