Final answer:
Tripling a vehicle's speed from 20 mph to 60 mph increases the braking and impact distances by a factor of 9, because both distances are proportional to the square of the speed.
Step-by-step explanation:
When the speed of a vehicle is tripled from 20 mph to 60 mph, not only does the impact speed increase, but also the total distance needed to come to a stop, which includes both braking distance and the distance traveled during the driver's reaction time, increases significantly. According to the basic physics of motion, both the braking distance and impact force are proportional to the square of the velocity. This means that when you triple the speed, the braking and impact distances increase by a factor of 9, since 3 squared is 9.
Therefore, tripling the speed from 20 mph to 60 mph would increase the impact and braking distance 9 times greater, assuming the driving conditions and vehicle braking efficiency remain constant.