1 A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to one end of a light elastic string of natural length 1.8 m and modulus of elasticity 1.35 mg N . The other end of the string is attached to a fixed point \(O\) on a smooth horizontal surface. \(P\) is held at rest at a point on the surface 3 m from \(O\). The particle is then released. Find
- the initial acceleration of \(P\),
- the speed of \(P\) at the instant the string becomes slack.