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\includegraphics[max width=\textwidth, alt={}, center]{16640429-198d-4ea9-a2f6-6e2ef6ac1b4a-12_282_1106_264_523} As shown in the diagram, a particle \(A\) of mass 1.6 kg lies on a horizontal plane and a particle \(B\) of mass 2.4 kg lies on a plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. The particles are connected by a light inextensible string which passes over a small smooth pulley \(P\) fixed at the top of the inclined plane. The distance \(A P\) is 2.5 m and the distance of \(B\) from the bottom of the inclined plane is 1 m . There is a barrier at the bottom of the inclined plane preventing any further motion of \(B\). The part \(B P\) of the string is parallel to a line of greatest slope of the inclined plane. The particles are released from rest with both parts of the string taut.

1. Given that both planes are smooth, find the acceleration of \(A\) and the tension in the string.
2. It is given instead that the horizontal plane is rough and that the coefficient of friction between \(A\) and the horizontal plane is 0.2 . The inclined plane is smooth. Find the total distance travelled by \(A\).
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