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

1. Find the distance \(A B\) and the value of \(d\).
   \(A B\) 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 \(B C\) is 2 m .
2. Find the speed with which the ball starts to move towards \(A\) and the time taken for the ball to travel from \(B\) to \(C\).
3. 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 \(C\).