Kinematics of motion in a straight line — practice question

Particle $P$ moves along the straight line from $A$ to $B$. After leaving $A$, its velocity at time $t\,\text{s}$ is given by $v\,\text{m s}^{-1}$, where $v = 0.04t^3 + ct^2 + kt$. The journey from $A$ to $B$ takes $5\,\text{s}$, and when it reaches $B$ its speed is $10\,\text{m s}^{-1}$. The distance $AB$ is $25\,\text{m}$.