6 One end of a light elastic string of natural length 1.25 m and modulus of elasticity 20 N is attached to a fixed point \(O\). A particle \(P\) of mass 0.5 kg is attached to the other end of the string. \(P\) is held at rest at \(O\) and then released. When the extension of the string is \(x \mathrm {~m}\) the speed of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(v ^ { 2 } = - 32 x ^ { 2 } + 20 x + 25\).
2. Find the maximum speed of \(P\).
3. Find the acceleration of \(P\) when it is at its lowest point.