A particle \(P\) of mass \(0.3\text{ kg}\) is connected by a light inextensible string to a particle \(Q\) of mass \(0.2\text{ kg}\). The string joining the two particles is taut and is parallel to a line of greatest slope of a rough plane which is inclined at an angle of \(30^\circ\) to the horizontal. A constant force of magnitude \(12\text{ N}\) acts on \(Q\) and pulls the particles up the plane. The \(12\text{ N}\) force acts parallel to a line of greatest slope of the plane (see diagram). The coefficient of friction between each of the particles and the plane is \(0.4\).

(a) Find the magnitude of the acceleration of the particles and the tension in the string.

(b) At the instant when the speed of the particles is \(2\text{ m s}^{-1}\), the string breaks.

Find the time it takes from the instant the string breaks until \(P\) comes to instantaneous rest.