What is the stopping distance if the car is initially traveling at speed 6.0v? assume that the acceleration due to the braking is the same in both cases?

The distance for any rectilinear motion at constant acceleration is:

d = v₀t + 0.5at²

where

v₀ is the initial velocity

So, if v₀ = 6v, and it stopped to 0 m/s, then the acceleration is equal to:

a = (0 - 6v) / t = - 6v/t

Thus,

d = (6v) (t) + (0.5) (-6v/t) (t²)

d = 6vt - 3t

d = 3t (2v - 1)