A particle \(P\) is initially at a distance of \(d = 16 m\) from point \(O\). The particle \(P\) moves with a velocity given by

\[\overrightarrow{v} = 5 \overrightarrow{PO} + 3\hat{i}\]

where \(\overrightarrow{PO}\) is a unit vector from \(P\) to \(O\) at any time t.

Initially \(\overrightarrow{PO}\) is perpendicular to \(\hat{i}\).

Find the time in second after which point \(P\) meets point \(O\).

**Details and Assumptions:**

\(\hat{i}\) is unit vector along the direction of x-axis.

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