Two particles, \(A\) and \(B\), of masses \(2.5\text{ kg}\) and \(3.5\text{ kg}\) respectively are at rest on a straight smooth horizontal track. Particle \(B\) is situated \(9\text{ m}\) from a vertical wall which is fixed at right angles to the track.

Particle \(A\) is projected directly towards \(B\) with a speed of \(3\text{ m s}^{-1}\). In the subsequent motion, \(A\) collides and coalesces with \(B\) to form particle \(C\). Particle \(C\) then collides directly with the wall and rebounds. The collision of \(C\) with the wall reduces the speed of \(C\) by \(25\%\).

(a) Find the speed of \(C\) after it rebounds from the wall.

(b) Hence find the time from the instant at which \(A\) and \(B\) collide until \(C\) is once again a distance of \(9\text{ m}\) from the wall.