A particle \(P\) moves so that its displacement, \(x\) metres from a fixed point \(O\), at time \(t\) seconds, is given by

\(x=\ln(5t+3).\)

(i) Find the value of \(t\) when the displacement of \(P\) is \(3\text{ m}\).

(ii) Find the velocity of \(P\) when \(t=0\).

(iii) Explain why, after passing through \(O\), the velocity of \(P\) is never negative.

(iv) Find the acceleration of \(P\) when \(t=0\).