1. A train travels along a straight horizontal track from station \(P\) to station \(Q\).

In a model of the motion of the train, at time \(t = 0\) the train starts from rest at \(P\), and moves with constant acceleration until it reaches its maximum speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) The train then travels at this constant speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) before finally moving with constant deceleration until it comes to rest at \(Q\). The time spent decelerating is four times the time spent accelerating.
The journey from \(P\) to \(Q\) takes 700 s .
Using the model,

1. sketch a speed-time graph for the motion of the train between the two stations \(P\) and \(Q\). The distance between the two stations is 15 km .
   Using the model,
2. show that the time spent accelerating by the train is 40 s ,
3. find the acceleration, in \(\mathrm { m } \mathrm { s } ^ { - 2 }\), of the train,
4. find the speed of the train 572s after leaving \(P\).
5. State one limitation of the model which could affect your answers to parts (b) and (c).