So after more asking around, someone's presented to me the idea that maximum velocity would be the same for acceleration and deceleration which is pretty obvious, but I didn't think to include this in the equation. Is this what you're getting at?
So therefore using ##v = at##:
##a_1 t_1 = a_2...
It does indeed seem wrong. So this is what I've done to prove this wrong:
Using ##D = \frac{at^2}{ 2}## and:
## a_1 = a_2 ##, so therefore:
##t_1 = t_2 ## and ##d_1 = d_2##
##T = 2 * t_1##, and therefore ##t_1 = \frac{T}{2}##
##D = 2 * d_1##
##D = at_1^2##
##= a (\frac{T}{2}^2)##
##=...
Fair. The wording could do with changing. Basically, I've badly implied that the reason why we're not coasting at a fixed speed is because the traversal needs to be done within the fastest time possible.
Note: Maths has always been kinda a weak point for me in school. Anyway.
From hereon I'm going to talk about this in the context of a train for simplicity, even though this is actually needed for an entirely different context - but I don't think this is relevant for the problem.
In terms of my...