I'm doing a research project on the mathematics of robotics. For this research project I need to use calculus somewhere in the project. My plan was to calculate the acceleration of the robot and find the velocity and position by integrating. I am currently using the following equations to find acceleration
Force = Torque / radius of wheel
acceleration = Force / mass
the problem is that the acceleration of a robot shouldn't be a constant as this equation finds, because at some point the acceleration should reach a max and gradually approach 0.
So, how would I go about finding the real acceleration of the robot? I think where i'm going wrong is plugging in static numbers for Torque, but I can not figure out how I would find the change in torque over time.
The specs for the motor I am using are here . Also, the mass of the robot is 135 pounds.