2 A particle of mass \(m \mathrm {~kg}\) moves horizontally in a straight line with speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t \mathrm {~s}\). The total resistance force on the particle is of magnitude \(m k v ^ { \frac { 3 } { 2 } } \mathrm {~N}\) where \(k\) is a positive constant. There are no other horizontal forces present. Initially \(v = 25\) and the particle is at a point O .

1. Show that \(v = 4 \left( k t + \frac { 2 } { 5 } \right) ^ { - 2 }\).
2. Find the displacement from O of the particle at time \(t\).
3. Describe the motion of the particle as \(t\) increases. Section B (48 marks)