7 A particle \(P\) of mass 0.5 kg moves upwards along a line of greatest slope of a rough plane inclined at an angle of \(40 ^ { \circ }\) to the horizontal. \(P\) reaches its highest point and then moves back down the plane. The coefficient of friction between \(P\) and the plane is 0.6 .

1. Show that the magnitude of the frictional force acting on \(P\) is 2.25 N , correct to 3 significant figures.
2. Find the acceleration of \(P\) when it is moving
   (a) up the plane,
   (b) down the plane.
3. When \(P\) is moving up the plane, it passes through a point \(A\) with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   (a) Find the length of time before \(P\) reaches its highest point.
   (b) Find the total length of time for \(P\) to travel from the point \(A\) to its highest point and back to \(A\).