Vehicle A weighs 3,000 pounds. Under ideal conditions traveling at 55 miles per hour, its braking distance is 200 feet. If it carries 3,000 pounds of extra weight, what is the new braking distance?
The exact same braking distance (200ft in your case)
The net external force responsible for accelerating your object to a stop is friction from the road on the tires. Assuming a flat, horizontal road, then the frictional force is directly proportional to weight by: f = (mu)n where n=mg
Long story short, mass cancels out and the acceleration is simply (mu)g regardless of how much weight is loaded in the vehicle. If the acceleration is the same and all other kinematic conditions are the same, you will calculate the same displacement.