A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds, \(t \geqslant 0\), the displacement of \(P\) from the origin \(O\) is \(x\) metres and the acceleration of \(P\) is \(\left( \frac { 7 } { 2 } - 2 x \right) \mathrm { m } \mathrm { s } ^ { - 2 }\), measured in the positive \(x\) direction. At time \(t = 0 , P\) passes through \(O\) moving with speed \(3 \mathrm {~ms} ^ { - 1 }\) in the positive \(x\) direction. Find the distance of \(P\) from \(O\) when \(P\) first comes to instantaneous rest.
(6)