A train is instructed to start at rest at station 1 and accelerate uniformly between points A and B, then coast with a uniform velocity between points B and C, and finally accelerate (slowing down) uniformly between points C and D until the train stops at station 2. The distances AB BC, and CD are all equal, and it takes 5.00 min to travel between the stations. Assume that the uniform accelerations have the same magnitude, even when they are opposite in direction.
I'm not sure which equation to use here...
The Attempt at a Solution
change in x from AB = change in x from CD as does the value for a with opposite signs.
I set the total distance between points A and D to an arbitrary number...lets say 9, set acceleration to an arbitrary number, lets say 1 m/min, and tried to find a number for time that would satisfy the problem. So after one min, the train would reach 1 m velocity, then 2 m velocity after 2 min, and would have then traveled 3 m total which is 1/3 of the total distance. This would end up taking 2 min (AB) + 2 min (BD) + 1.5 min (CD) = 6.5 min to travel the distance of 9. I would need to find a value time where the train travels the same for BC as AB over a course of time that would make its distance work in 5 minutes total. Maybe I could use a common scale factor that take everything down proportionally. I think I made it more confusing with all that I just said...lol.
Surely there is a much simpler way to think it through?