6. A train starts from rest at a station \(A\) and moves along a straight horizontal track. For the first 10 s , the train moves with constant acceleration \(1.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). For the next 24 s it moves at a constant acceleration \(0.75 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). It then moves with constant speed for \(T\) seconds. Finally it slows down with constant deceleration \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it comes to a rest at station \(B\).

1. Show that, 34 s after leaving \(A\), the speed of the train is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Sketch a speed-time graph to illustrate the motion of the train as it moves from \(A\) to \(B\).
3. Find the distance moved by the train during the first 34 s of its journey from \(A\). The distance from \(A\) to \(B\) is 3 km .
4. Find the value of \(T\).