A five$-$axis robot needs to perform a two$-$stage movement. In the first stage, the first joint

needs to go from initial angle of $25$ deg to a final angle of $11$ deg in $5$ seconds. In the second

stage, the first joint needs to go from $11$ deg to $115$ deg in $3$ seconds.

The robot is at rest at the start of the whole process. The angular speed needs to be pi$/6$

rad$/$s when passing $11$ deg. It will be fully stopped at $115$ deg. Find the corresponding third$-$order

polynomials for both stage $1$ and stage $2.$

Please also explain solving the resulting equations. Thank you!