7 A light elastic string has natural length 3 m and modulus of elasticity 45 N . A particle \(P\) of weight 6 N is attached to the mid-point of the string. The ends of the string are attached to fixed points \(A\) and \(B\) which lie in the same vertical line with \(A\) above \(B\) and \(A B = 4 \mathrm {~m}\). The particle \(P\) is released from rest at the point 1.5 m vertically below \(A\).

1. Calculate the distance \(P\) moves after its release before first coming to instantaneous rest at a point vertically above \(B\). (You may assume that at this point the part of the string joining \(P\) to \(B\) is slack.)
2. Show that the greatest speed of \(P\) occurs when it is 2.1 m below \(A\), and calculate this greatest speed.
3. Calculate the greatest magnitude of the acceleration of \(P\).