A ball moves on the horizontal surface of a billiards table with deceleration of constant magnitude $d{\text{ }}m{\text{ }}{s^{ - 2}}$. The ball starts at $A$ with speed $1.4{\text{ }}m{\text{ }}{s^{ - 1}}$ and reaches the edge of the table at $B$, $1.2{\text{ }}s$ later, with speed $1.1{\text{ }}m{\text{ }}{s^{ - 1}}$.

a) Find the distance $AB$ and the value of $d$.

$AB$ is at right angles to the edge of the table containing $B$. The table has a low wall along each of its edges and the ball rebounds from the wall at $B$ and moves directly towards $A$. The ball comes to rest at $C$ where the distance $BC$ is $2{\text{ }}m$.

b) Find the speed with which the ball starts to move towards $A$ and the time taken for the ball to travel from $B$ to $C$.

c) Sketch a velocity-time graph for the motion of the ball, from the time the ball leaves $A$ until it comes to rest at $C$, showing on the axes the values of the velocity and the time when the ball is at $A$, at $B$ and at $C$.