Sorry for disturbing you again. So I have totally understand what you explained to me . But after engaging a little bit I think i forgot to mention an important thing.I have regarded that acceleration is equal to deceleration for my convenience so I did my calculations only for acceleration form and state speed. So my formulation of the total time is the the total time within state speed motion and acceleration motion this formulation would be the above. Because t in acceleration is 2dx/ux ( dx=1/2at2 and i put a as ux/t) and the time in state speed which is x/u. If i abstract the first one i get the total time travelled only in state speed . Then I add the u/a and I get the total travelled distance in acceleration and state speed. So thats why I was asking what will happen if xi>=2x, But now you got me thinking that is better if I analyse all the movement as you explained.