Kinematics of motion in a straight line — practice question

A particle begins at rest at point $O$ and travels along a straight line. At time $t$ after leaving $O$, its acceleration is $a\,\text{m s}^{-2}$, with $a = kt^{\frac{1}{2}}$ for $0 \leq t \leq 9$, where $k$ is constant. When $t = 9$, the particle's velocity is $1.8\,\text{m s}^{-1}$. For $t > 9$, the velocity $v\,\text{m s}^{-1}$ is $v = 0.2(t - 9)^2 + 1.8$.