A robot moves along a straight line for $3 \mathrm{s}$. The displacement of the robot, $s \mathrm{m}$, from its initial position is given by $s=A{t}^3+B{t}^2+Ct$ for constants $A, B$ and $C,$ where $t$ is measured in seconds and $0<t<3$. The robot starts with velocity $2 \mathrm{m}{ \mathrm{s}}^{-1}$. It travels $6 \mathrm{m}$ before coming to rest at time $t=3 .$ Work out the values of $A, B$ and $C.$