5 A particle \(P\) moves in a straight line starting from a point \(O\) and comes to rest 35 s later. At time \(t \mathrm {~s}\) after leaving \(O\), the velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of \(P\) is given by $$\begin{array} { l l } v = \frac { 4 } { 5 } t ^ { 2 } & 0 \leqslant t \leqslant 5
v = 2 t + 10 & 5 \leqslant t \leqslant 15
v = a + b t ^ { 2 } & 15 \leqslant t \leqslant 35 \end{array}$$ where \(a\) and \(b\) are constants such that \(a > 0\) and \(b < 0\).

1. Show that the values of \(a\) and \(b\) are 49 and - 0.04 respectively.
2. Sketch the velocity-time graph.
   \includegraphics[max width=\textwidth, alt={}, center]{f3ddfde8-b678-4c3a-a9a6-d984c2c38bd9-09_689_1323_349_452}
3. Find the total distance travelled by \(P\) during the 35 s .
   \includegraphics[max width=\textwidth, alt={}, center]{f3ddfde8-b678-4c3a-a9a6-d984c2c38bd9-10_487_506_260_817} Two particles of masses 1.2 kg and 0.8 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest with both particles 0.64 m above the floor (see diagram). In the subsequent motion the 0.8 kg particle does not reach the pulley.
4. Show that the acceleration of the particles is \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and find the tension in the string.
5. Find the total distance travelled by the 0.8 kg particle during the first second after the particles are released.