We will use the formula:
2as = v² - u²; where the final velocity v is 0, the distance s will be represented by x and the initial velocity will be represented by v. So:
2ax = -v²
x₁ = 1/2 av²
for the distance it takes to stop, let's see what happens when we double the value v
x₂ = 1/2 A (2v)² = 4(1/2 * av²)
Now divide the formulae, getting
x₂ / x₁ =
(4(1/2 * av²)) / (1/2 av²) = 4
Doing the division, everything cancels out except for the value 4. So if your speed doubles, the stopping distance quadruples, or becomes 4 times the original.
