Lets see if I can explain it using a simple example. Suppose you can decrease the speed of the car at a rate of 10 mph every second.
No, lets use feet per second to avoid the conversions... hours are a pita
Suppose you can slow down a car 10 feet per second every second.
Now, if the car is going 50 feet per second, it's going to take 5 seconds to stop.
If the car is going 100 feet per second, it's going to take 10 seconds to stop.
Doubling the speed doubles the time it takes to stop.
Now the tricky part. If it went from 50 feet per second to 0 feet per second smoothly, it averaged 25 feet per second. Over 5 seconds, that means it traveled 125 feet.
If it went from 100 feet per second to 0 feet per second smoothly, it averaged 50 feet per second for 10 seconds, and traveled 500 feet.