4. Two trains \(M\) and \(N\) are moving in the same direction along parallel straight horizontal tracks. At time \(t = 0 , M\) overtakes \(N\) whilst they are travelling with speeds \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. Train \(M\) overtakes train \(N\) as they pass a point \(X\) at the side of the tracks. After overtaking \(N\), train \(M\) maintains its speed of \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T\) seconds and then decelerates uniformly, coming to rest next to a point \(Y\) at the side of the tracks. After being overtaken, train \(N\) maintains its speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 25 s and then decelerates uniformly, also coming to rest next to the point \(Y\). The times taken by the trains to travel between \(X\) and \(Y\) are the same.

1. Sketch, on the same diagram, the speed-time graphs for the motions of the two trains between \(X\) and \(Y\). Given that \(X Y = 975 \mathrm {~m}\),
2. find the value of \(T\).