7 A cyclist starts from rest at a point \(O\) and travels along a straight path. At time \(t \mathrm {~s}\) after starting, the displacement of the cyclist from \(O\) is \(x \mathrm {~m}\), and the acceleration of the cyclist is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), where \(a = 0.6 x ^ { 0.2 }\).

1. Find an expression for the velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) of the cyclist in terms of \(x\).
2. Show that \(t = 2.5 x ^ { 0.4 }\).
3. Find the distance travelled by the cyclist in the first 10 s of the journey.