3 A particle \(P\) starts from a fixed point \(O\) and moves in a straight line. When the displacement of \(P\) from \(O\) is \(x \mathrm {~m}\), its velocity is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and its acceleration is \(\frac { 1 } { x + 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Given that \(v = 2\) when \(x = 0\), use integration to show that \(v ^ { 2 } = 2 \ln \left( \frac { 1 } { 2 } x + 1 \right) + 4\).
2. Find the value of \(v\) when the acceleration of \(P\) is \(\frac { 1 } { 4 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\).