7 A particle \(X\) travels in a straight line. The velocity of \(X\) at time \(t\) s after leaving a fixed point \(O\) is denoted by \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where $$v = - 0.1 t ^ { 3 } + 1.8 t ^ { 2 } - 6 t + 5.6$$ The acceleration of \(X\) is zero at \(t = p\) and \(t = q\), where \(p < q\).

1. Find the value of \(p\) and the value of \(q\).
   It is given that the velocity of \(X\) is zero at \(t = 14\).
2. Find the velocities of \(X\) at \(t = p\) and at \(t = q\), and hence sketch the velocity-time graph for the motion of \(X\) for \(0 \leqslant t \leqslant 15\).
3. Find the total distance travelled by \(X\) between \(t = 0\) and \(t = 15\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.