2. At time \(t = 0\) a particle \(P\) leaves the origin \(O\) and moves along the \(x\)-axis. At time \(t\) seconds the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where
$$v = 8 t - t ^ { 2 }$$
- Find the maximum value of \(v\).
- Find the time taken for \(P\) to return to \(O\).