A particle P of mass 0.25 kg moves in a straight line on a smooth horizontal surface. P starts at the point O with speed 10ms^-1 and moves towards a fixed point A on the line.

At time is the displacement of P from O is xm and the velocity of P is v .

A resistive force of magnitude (5 - x)N acts on P in the direction towards O.

i. Form a differential equation in v and x. By solving this differential equation, show that v = 10 - 2x.

ii. Find x in terms of t, and hence show that the particle is always less than 5m from O.