Question

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?

Answer 1

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)