Use wheels that are 1.187 x the diameter (10m/8.427m)or larger than your current drive wheels. It might be a good idea to use 1.25 x the diameter to compensate for any decrease in speed due to the additional loading and to provide a margin for error.
If you're using servos, a braking system should be unnecessary. The servos should hold their position when their speed is commanded to zero (this can be harder to accomplish than you might think.) Once the vehicle is stopped, turning off the power to the servos should hold it in position.
For most accurate results you might want to consider trapezoidal speed curve as your braking system.
This is often used when driving stepper motors to prevent skipped steps that can happen when you try to accelerate the motor too fast. Skipped steps can produce strange, unpredictable results.
When driving servos, the speed/time curve translates directly into pulse width input to the servos. e.g. A 1.5ms pulse commands 0 speed, a 2ms pulse commands full speed, and a .5ms pulse commands full speed in reverse. (check the pulse widths are correct, I'm going strictly from memory). Acceleration is the rate of change (slope) of the pulse width.
Note: in unmodified servos, the input pulse width represents a position error. The servos drive to a position (rotation angle from center position) relative to the pulse width. Servos modified for continuous rotation use a fixed position signal equivalent to the center position. This makes the input pulse width a speed command rather than a displacement command.
Edit: OOPS! That should have been 1.0ms for full speed in reverse. Speed vs pulse width is usually fairly linear, but different manufacturer/model servos (and individual servos to a lesser extent) can vary greatly.