At time \(t = 0\), a particle \(P\) is at the origin \(O\) moving with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) along the \(x\)-axis in the positive \(x\)-direction. At time \(t\) seconds \(( t > 0 )\), the acceleration of \(P\) has magnitude \(\frac { 3 } { ( t + 1 ) ^ { 2 } } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and is directed towards \(O\).
Show that at time \(t\) seconds the velocity of \(P\) is \(\left( \frac { 3 } { t + 1 } - 1 \right) \mathrm { m } \mathrm { s } ^ { - 1 }\).
Find, to 3 significant figures, the distance of \(P\) from \(O\) when \(P\) is instantaneously at rest.