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.

Question

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.

oobleck · Answer

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.