From a standstill, acceleration is limited by three things:
- Torque/gearing
- CoF of the wheels on the carpet/floor
- Stability: determined by the height of the CoG compared to wheelbase
A bit more detail:
- Torque: Calculate the combined torque of the drive motors at the maximum current you're willing to draw. Multiply by the gear ratio. Divide by the wheel radius. Divide by the mass of the robot. About 80% of this is the maximum acceleration you can achieve without popping breakers or browning out.
- CoF: Multiply the CoF of your driven wheels by the fraction of the weight of the robot carried by those wheels, and multiply that by the acceleration of gravity. If you try to accelerate faster than this, the wheels slip on the carpet/floor.
- Stability: Divide the horizontal distance from the rear (front) wheels to the CoG by the vertical distance from this axle to the CoG, and multiply by the acceleration of gravity. If you try to accelerate (decelerate) faster than this, the robot winds up laying on its back (face).
Once you're moving, the maximum acceleration is reduced, as noted by several previous posters.