6 A particle moves in a straight line. It starts from rest, at time \(t = 0\), and accelerates at \(0.6 t \mathrm {~ms} ^ { - 2 }\) for 4 s , reaching a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particle then travels at \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 11 s , and finally slows down, with constant deceleration, stopping after a further 5 s .

1. Show that \(V = 4.8\).
2. Sketch a velocity-time graph for the motion.
   \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-08_2722_40_107_2010}
3. Find an expression, in terms of \(t\), for the velocity of the particle for \(15 \leqslant t \leqslant 20\).
4. Find the total distance travelled by the particle.
   \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-10_592_608_251_731} Two particles, \(A\) and \(B\), of masses 3 kg and 5 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles are held with the string taut and its straight parts vertical. Particle \(A\) is 1 m above a horizontal plane, and particle \(B\) is 2 m above the plane (see diagram). The particles are released from rest. In the subsequent motion, \(A\) does not reach the pulley, and after \(B\) reaches the plane it remains in contact with the plane.
5. Find the tension in the string and the time taken for \(B\) to reach the plane.
   \includegraphics[max width=\textwidth, alt={}, center]{3a6ecf05-127f-4ddf-959e-233f6bae9171-10_2718_42_107_2007}
6. Find the time for which \(A\) is at least 3.25 m above the plane.
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