A particle \(P\) moves on the \(x\)-axis. The acceleration of \(P\) at time \(t\) seconds is \(( t - 4 ) \mathrm { m } \mathrm { s } ^ { - 2 }\) in the positive \(x\)-direction. The velocity of \(P\) at time \(t\) seconds is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When \(t = 0 , v = 6\).
Find
\(v\) in terms of \(t\),
the values of \(t\) when \(P\) is instantaneously at rest,
the distance between the two points at which \(P\) is instantaneously at rest.