5. A train is travelling at \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) on a straight horizontal track. The driver sees a red signal 135 m ahead and immediately applies the brakes. The train immediately decelerates with constant deceleration for 12 s , reducing its speed to \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The driver then releases the brakes and allows the train to travel at a constant speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for a further 15 s . He then applies the brakes again and the train slows down with constant deceleration, coming to rest as it reaches the signal.

1. Sketch a speed-time graph to show the motion of the train,
2. Find the distance travelled by the train from the moment when the brakes are first applied to the moment when its speed first reaches \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
3. Find the total time from the moment when the brakes are first applied to the moment when the train comes to rest.