How do I solve a maze using velocity and acceleration?
At any point, the state of the system is a pair $(p,v)$ where $p$ is the current position and $v$ is the current velocity vector.  At any state, there are 8 possible actions (transitions out of that state, to another state).  Search over this state space using any algorithm for searching state spaces to find the lowest-cost path from the start state to the desired end state; for example, you could use BFS, A*, etc.  This should solve the problem in a clean, straightforward, and efficient way.