6
\includegraphics[max width=\textwidth, alt={}, center]{f08a4870-9466-4f8b-bd0f-431fb1803514-08_661_1244_262_452} The diagram shows the velocity-time graphs for two particles, \(P\) and \(Q\), which are moving in the same straight line. The graph for \(P\) consists of four straight line segments. The graph for \(Q\) consists of three straight line segments. Both particles start from the same initial position \(O\) on the line. \(Q\) starts 2 seconds after \(P\) and both particles come to rest at time \(t = T\). The greatest velocity of \(Q\) is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find the displacement of \(P\) from \(O\) at \(t = 10\).
2. Find the velocity of \(P\) at \(t = 12\).
3. Given that the total distance covered by \(P\) during the \(T\) seconds of its motion is 49.5 m , find the value of \(T\).
4. Given also that the acceleration of \(Q\) from \(t = 2\) to \(t = 6\) is \(1.75 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find the value of \(V\) and hence find the distance between the two particles when they both come to rest at \(t = T\).
   \includegraphics[max width=\textwidth, alt={}, center]{f08a4870-9466-4f8b-bd0f-431fb1803514-10_392_529_262_808} A particle \(P\) of mass 0.2 kg rests on a rough plane inclined at \(30 ^ { \circ }\) to the horizontal. The coefficient of friction between the particle and the plane is 0.3 . A force of magnitude \(T \mathrm {~N}\) acts upwards on \(P\) at \(15 ^ { \circ }\) above a line of greatest slope of the plane (see diagram).
5. Find the least value of \(T\) for which the particle remains at rest.
   The force of magnitude \(T \mathrm {~N}\) is now removed. A new force of magnitude 0.25 N acts on \(P\) up the plane, parallel to a line of greatest slope of the plane. Starting from rest, \(P\) slides down the plane. After moving a distance of \(3 \mathrm {~m} , P\) passes through the point \(A\).
6. Use an energy method to find the speed of \(P\) at \(A\).