Particles $A$ and $B$ are moving along horizontal straight lines which lie in the west east direction. At a certain time, $A$ passes a point $P$ moving to the east with speed $5$ ms$^{-1}$ and constant acceleration $1$ ms$^{-2}$. Simultaneously, $B$ passes a point $Q$ east of $P$ with speed $4$ ms$^{-1}$ towards the west but with constant acceleration $2$ ms$^{-2}$ towards the east. Given that the distance $PQ$ is $28$ m, Calculate
a) The distance of $A$ from $P$ when $B$ reverse direction
b) The time taken after the start for $A$ to overtake
c) The further time taken for $B$ to overtake $A$