5 Each of two light elastic strings, \(S _ { 1 }\) and \(S _ { 2 }\), has modulus of elasticity 16 N . The string \(S _ { 1 }\) has natural length 0.4 m and the string \(S _ { 2 }\) has natural length 0.5 m . One end of \(S _ { 1 }\) is attached to a fixed point \(A\) of a smooth horizontal table and the other end is attached to a particle \(P\) of mass 0.5 kg . One end of \(S _ { 2 }\) is attached to a fixed point \(B\) of the table and the other end is attached to \(P\). The distance \(A B\) is 1.5 m . The particle \(P\) is held at \(A\) and then released from rest.

1. Find the speed of \(P\) at the instant that \(S _ { 2 }\) becomes slack.
2. Find the greatest distance of \(P\) from \(A\) in the subsequent motion.