I am sure others will have more thorough anwers, but I will try to contribute:
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If we assume the brakes "lock" the wheels to create a skid mark, then the
above result shows that the stopping distance does NOT depend on the car's
mass.
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I believe the assumption and the braking model are both a part of the problem. If we do a Force analysis, we find the masses 'cancel out' when analyzing the acceleration of the car.
F_net=F_fr
ma =u * F_n
ma = u * ma_g (assuming we are on a horizontal surface)
here the masses cancel.
*However*, this is assuming that the frictional force stopping the car is caused by the frictional interaction between the wheels & the ground. This is not true, even when brakes lock up.
The frictional breaking force exists between the pads/calipers and disks/drums. This force does Not change Due to the mass of the car. It is a design of the breaking system.
Regarding large trucks, I have been told two versions. I can only relay what I've heard.
1-They are able to use their drive-train in a funky reverse mode to slow then down.
2-Air brakes-- I do not know any more.
--I know my response here is very un-satisfying.