Kinematics of motion in a straight line — practice question

A particle travels in a straight line, beginning at point $O$, before coming to instantaneous rest at point $X$. For time $t$ s after leaving $O$, the velocity $v\,\text{m s}^{-1}$ of the particle is defined by $v = 7.2t^2 \quad 0 \leq t \leq 2,$ $v = 30.6 - 0.9t \quad 2 \leq t \leq 8,$ $v = \frac{1600}{t^2} + kt \quad 8 \leq t,$ where $k$ is a constant. It is stated that there is no instantaneous change in velocity at $t = 8$.