3
\includegraphics[max width=\textwidth, alt={}, center]{8d64372d-0b9a-4b93-8c41-7096c813f714-2_443_825_755_661} A particle \(P\) is projected from the top of a smooth ramp with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and travels down a line of greatest slope. The ramp has length 6.4 m and is inclined at \(30 ^ { \circ }\) to the horizontal. Another particle \(Q\) is released from rest at a point 3.2 m vertically above the bottom of the ramp, at the same instant that \(P\) is projected (see diagram). Given that \(P\) and \(Q\) reach the bottom of the ramp simultaneously, find

1. the value of \(u\),
2. the speed with which \(P\) reaches the bottom of the ramp.
   \includegraphics[max width=\textwidth, alt={}, center]{8d64372d-0b9a-4b93-8c41-7096c813f714-3_609_1539_255_303} The diagram shows the velocity-time graphs for the motion of two particles \(P\) and \(Q\), which travel in the same direction along a straight line. \(P\) and \(Q\) both start at the same point \(X\) on the line, but \(Q\) starts to move \(T\) s later than \(P\). Each particle moves with speed \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for the first 20 s of its motion. The speed of each particle changes instantaneously to \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) after it has been moving for 20 s and the particle continues at this speed.