3 A particle \(P\) moves on the positive \(x\)-axis in simple harmonic motion. The centre of the motion is a distance \(d \mathrm {~m}\) from the origin \(O\), where \(0 < d < 6.5\). The points \(A\) and \(B\) are on the positive \(x\)-axis, with \(O A = 6.5 \mathrm {~m}\) and \(O B = 7.5 \mathrm {~m}\). The magnitude of the acceleration of \(P\) when it is at \(B\) is twice the magnitude of the acceleration of \(P\) when it is at \(A\).

1. Find \(d\).
   The period of the motion is \(\pi \mathrm { s }\) and the maximum acceleration of \(P\) during the motion is \(10 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2. Find the speed of \(P\) when it is 7 m from \(O\).
3. Find the time taken by \(P\) to travel directly from \(A\) to \(B\).