5. A particle \(P\) moves on the \(x\)-axis. The acceleration of \(P\) at time \(t\) seconds is \(( 4 t - 8 ) \mathrm { m } \mathrm { s } ^ { - 2 }\), measured in the direction of \(x\) increasing. The velocity of \(P\) at time \(t\) seconds is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Given that \(v = 6\) when \(t = 0\), find

1. \(v\) in terms of \(t\),
2. the distance between the two points where \(P\) is instantaneously at rest.