Question

A person is driving a car with speed of vo. The person brakes to stop over time t and distance d. The magnitude of the person acceleration is a. If the person doubles her initial velocity , how much distance does she travels as she stops

Answer 1

The distance traveled by a car to the rest

$$d=\frac{v_0^2}{2a}$$

If the person doubles her initial velocity then she's distance traveled to the stop increases by factor four:

$$d'=\frac{(2v_0)^2}{2a}=4\frac{v_0^2}{2a}=4d$$