A particle P of mass 0.5 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 16 N. The other end of the string is attached to a fixed point O. The particle P is released from rest at the point 0.8 m vertically below O. When the extension of the string is x m, the downwards velocity of P is v m s⁻¹ and a force of magnitude 25x² N opposes the motion of P.

1. (i)Show that, when P is moving downwards, v(dv/dx) = 10 – 40x - 50x².[2]
2. (ii)For the instant when P has its greatest downwards speed, find the kinetic energy of P and the elastic potential energy stored in the string.[6]