- A particle \(P\) moves on the positive \(x\)-axis. When the displacement of \(P\) from \(O\) is \(x\) metres, its acceleration is \(( 6 - 4 x ) \mathrm { m } \mathrm { s } ^ { - 2 }\), measured in the direction of \(x\) increasing. Initially \(P\) is at \(O\) and the velocity of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction \(O x\).
Find the distance of \(P\) from \(O\) when \(P\) is instantaneously at rest.