5 Two particles, \(P\) and \(Q\), are connected by a string that passes over a fixed smooth peg, as shown in the diagram. The mass of \(P\) is 5 kg and the mass of \(Q\) is 3 kg .
\includegraphics[max width=\textwidth, alt={}, center]{7ac7dfd0-4c3e-4eb7-920f-ce5b24ad1281-3_209_433_1009_808} The particles are released from rest in the position shown.

1. By forming an equation of motion for each particle, show that the magnitude of the acceleration of each particle is \(2.45 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2. Find the tension in the string.
3. State two modelling assumptions that you have made about the string.
4. Particle \(P\) hits the floor when it has moved 0.196 metres and \(Q\) has not reached the peg.
   1. Find the time that it takes \(P\) to reach the floor.
   2. Find the speed of \(P\) when it hits the floor.