Two trains $A$ and $B$ each of length $400 \,m$ are moving on two parallel tracks with a uniform speed $72\, km\, h^{-1}$ in the same direction with $A$ ahead of $B$. The driver of $B$ decides to overtake $A$ and accelerates by $1\, m \,s^{-2}$. If after $50\, s$, the guard of $B$ just brushes past $A$, what was the original distance between them ?