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\includegraphics[max width=\textwidth, alt={}, center]{ba29ddb2-3558-4be1-a8a8-134e27a70149-10_220_609_260_769} A particle \(P\) of mass 0.3 kg rests on a rough plane inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 7 } { 25 }\). A horizontal force of magnitude 4 N , acting in the vertical plane containing a line of greatest slope of the plane, is applied to \(P\) (see diagram). The particle is on the point of sliding up the plane.

1. Show that the coefficient of friction between the particle and the plane is \(\frac { 3 } { 4 }\).
   The force acting horizontally is replaced by a force of magnitude 4 N acting up the plane parallel to a line of greatest slope.
2. Find the acceleration of \(P\).
3. Starting with \(P\) at rest, the force of 4 N parallel to the plane acts for 3 seconds and is then removed. Find the total distance travelled until \(P\) comes to instantaneous rest.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.