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\includegraphics[max width=\textwidth, alt={}, center]{c6bac5bf-960e-4c3d-b9fa-c52de66ba719-4_652_1068_255_500} The diagram shows the ( \(t , v\) ) graphs for two particles \(A\) and \(B\) which move on the same straight line. The units of \(v\) and \(t\) are \(\mathrm { ms } ^ { - 1 }\) and s respectively. Both particles are at the point \(S\) on the line when \(t = 0\). The particle \(A\) is initially at rest, and moves with acceleration \(0.18 t \mathrm {~ms} ^ { - 2 }\) until the two particles collide when \(t = 16\). The initial velocity of \(B\) is \(U \mathrm {~ms} ^ { - 1 }\) and \(B\) has variable acceleration for the first five seconds of its motion. For the next ten seconds of its motion \(B\) has a constant velocity of \(9 \mathrm {~ms} ^ { - 1 }\); finally \(B\) moves with constant deceleration for one second before it collides with \(A\).

1. Calculate the value of \(t\) at which the two particles have the same velocity. For \(0 \leqslant t \leqslant 5\) the distance of \(B\) from \(S\) is \(\left( U t + 0.08 t ^ { 3 } \right) \mathrm { m }\).
2. Calculate \(U\) and verify that when \(t = 5 , B\) is 25 m from \(S\).
3. Calculate the velocity of \(B\) when \(t = 16\). \section*{END OF QUESTION PAPER}