Question

Three cars (car F, car G, and car H) are moving with the same velocity when the driver suddenly slams on the brakes, locking the wheels. The most massive car is car F, the least massive is car H, and all three cars have identical tires.

(a) Which car travels the longest distance to skid to a stop?
They all travel the same distance.
For all cars, ƒ = μN and N = F(g) = mg, therefore ƒ = μmg. Also, inertia is a property of matter and increases linearly. The more massive car has more inertia carrying it forward, but also more friction trying to stop it, so the two cancel out and all three cars will need the same distance to stop.

Answer 1

you're right. All three cars will travel the same distance to the bank to stop. This is because the stopping distance of a car depends on the friction between the tires and the road surface, which in turn is determined by the normal force and the coefficient of friction. Since all three cars have the same tires and are traveling at the same speed, they will experience the same amount of friction when the driver applies the brakes. A more massive car, the F, has more inertia, but also has more friction when trying to stop it, so the two effects balance out. Also, car H, which has less mass, has less inertia but also less friction, so both effects cancel out for this car as well. Therefore, all three vehicles will travel the same distance up the coast to the stopping point.