For a robotics project I wanted to find the optimal gear ratio for my robot to travel 10 meters. Unfortunately. the acceleration is nonconstant, and that proved to make my life much harder. I think I have most of it figured out, and the only part left is to find the correlation between the acceleration and velocity graph to the acceleration/velocity/position to time graph.
The robot with mass m and wheels that have a radius of r is allowed to accelerate on a surface with negligible friction. It uses 4 motors that have a free speed of Vfree rpm, and a stall torque of Tstall. The graph is included below. How can I find the time taken for this robot to travel x meters? I was able to turn the torque to angular velocity graph into an acceleration to velocity graph, but I got stuck trying to transform it into a distance to time or even a velocity to time graph.