7 A particle moves in a straight line, starting from rest at a point \(O\), and comes to instantaneous rest at a point \(P\). The velocity of the particle at time \(t \mathrm {~s}\) after leaving \(O\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where $$v = 0.6 t ^ { 2 } - 0.12 t ^ { 3 }$$

1. Show that the distance \(O P\) is 6.25 m .
   On another occasion, the particle also moves in the same straight line. On this occasion, the displacement of the particle at time \(t \mathrm {~s}\) after leaving \(O\) is \(s \mathrm {~m}\), where $$s = k t ^ { 3 } + c t ^ { 5 }$$ It is given that the particle passes point \(P\) with velocity \(1.25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t = 5\).
2. Find the values of the constants \(k\) and \(c\).
3. Find the acceleration of the particle at time \(t = 5\).
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