This technical note studies the following version of the Traveling Salesperson Problem (TSP) for a double integrator with bounded velocity and bounded control inputs: given a set of points in R-d, find the fastest tour over the point set. We first give asymptotic bounds on the time taken to complete such a tour in the worst case. Then, we study a stochastic version of the TSP for a double integrator in R-2 and R-3, where we propose novel algorithms that asymptotically perform within a constant factor of the optimal strategy with probability one. Lastly, we study a dynamic TSP in R-2 and R-3, where we propose novel stabilizing algorithms whose performances are within a constant factor from the optimum.