the work done against the frictional force acting on \(B\),
the loss of potential energy of the system,
the gain in kinetic energy of the system.
At the instant when \(B\) has moved 0.9 m the string breaks. \(A\) is at a height of 0.54 m above a horizontal floor at this instant.
(ii) Find the speed with which \(A\) reaches the floor.
\(6 \quad A B C\) is a line of greatest slope of a plane inclined at angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.28\) and \(\cos \alpha = 0.96\). The point \(A\) is at the top of the plane, the point \(C\) is at the bottom of the plane and the length of \(A C\) is 5 m . The part of the plane above the level of \(B\) is smooth and the part below the level of \(B\) is rough. A particle \(P\) is released from rest at \(A\) and reaches \(C\) with a speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The coefficient of friction between \(P\) and the part of the plane below \(B\) is 0.5 . Find
(i) the acceleration of \(P\) while moving
from \(A\) to \(B\),
from \(B\) to \(C\),
(ii) the distance \(A B\),
(iii) the time taken for \(P\) to move from \(A\) to \(C\).