Answer
Please see the work below.
Work Step by Step
Let us assume that on stopping the car, its K.E is converted to frictional heat that is $q=\frac{1}{2}mv^2$
We know that the amount of generated is directly proportional to braking distance. Mathematically, we can express it as
$d \space \alpha \space q$
and $d \space \alpha \space v^2$
That's why , when v increases to 2v, d becomes four times.
