6 A particle \(A\) is projected vertically upwards from level ground with an initial speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At the same instant a particle \(B\) is released from rest 15 m vertically above \(A\). The mass of one of the particles is twice the mass of the other particle. During the subsequent motion \(A\) and \(B\) collide and coalesce to form particle \(C\).
Find the difference between the two possible times at which \(C\) hits the ground.
\(7 \quad\) A particle \(P\) moving in a straight line starts from rest at a point \(O\) and comes to rest 16 s later. At time \(t \mathrm {~s}\) after leaving \(O\), the acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) of \(P\) is given by
$$\begin{array} { l l }
a = 6 + 4 t & 0 \leqslant t < 2 , \\
a = 14 & 2 \leqslant t < 4 , \\
a = 16 - 2 t & 4 \leqslant t \leqslant 16 .
\end{array}$$
There is no sudden change in velocity at any instant.
- Find the values of \(t\) when the velocity of \(P\) is \(55 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Complete the sketch of the velocity-time diagram.
\includegraphics[max width=\textwidth, alt={}, center]{41e63d05-d109-47dc-80a6-927953e3e607-11_511_1054_351_584} - Find the distance travelled by \(P\) when it is decelerating.
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