# math

Train traveling between two stations. The train starts from rest and accelerates uniformly for 150 seconds. It then travels at a constant speed for 300 seconds and finally decelerates uniformly for 200 seconds.
Given that the distance between the two stations is 10450m, calculate the:
(a) Maximum speed, in km/h, the train attained;
(b) Acceleration, (c) Distance the train traveled during the last 100 seconds;
(d) Time the train takes to travel the first half of the journey.

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1. If it accelerates at a m/s^2, then it reaches a top speed of 150a and travels 1/2 a*150^2 meters
Then it decelerates at 3/4 a for 200 seconds, and travels 150a*200 - 1/2 * 3/4 a * 200^2 meters
So, the total distance traveled is
1/2 a * 150^2 + 150a*300 + 150a*200 - 1/2 * 3/4 a * 200^2 = 10450
a = 11/75 m/s^2

See what you can do with that to answer the other bits.

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