6
\includegraphics[max width=\textwidth, alt={}, center]{a9f3480e-7a8a-497d-a26a-b2aba9b05512-4_712_529_264_810}
Particles \(P\) and \(Q\), of masses 0.55 kg and 0.45 kg respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed pulley. The particles are held at rest with the string taut and its straight parts vertical. Both particles are at a height of 5 m above the ground (see diagram). The system is released.
- Find the acceleration with which \(P\) starts to move.
The string breaks after 2 s and in the subsequent motion \(P\) and \(Q\) move vertically under gravity.
- At the instant that the string breaks, find
(a) the height above the ground of \(P\) and of \(Q\),
(b) the speed of the particles. - Show that \(Q\) reaches the ground 0.8 s later than \(P\).
\(7 \quad\) A particle \(P\) starts from rest at the point \(A\) at time \(t = 0\), where \(t\) is in seconds, and moves in a straight line with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 10 s . For \(10 \leqslant t \leqslant 20 , P\) continues to move along the line with velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v = \frac { 800 } { t ^ { 2 } } - 2\). Find - the speed of \(P\) when \(t = 10\), and the value of \(a\),
- the value of \(t\) for which the acceleration of \(P\) is \(- a \mathrm {~m} \mathrm {~s} ^ { - 2 }\),
- the displacement of \(P\) from \(A\) when \(t = 20\).
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