Cars can slow down much, much faster than they can speed up. Look at any 0-60 and 60-0 times in car reviews.
If there is any situation when you can see a potential accident and speeding up "saves you", then you also have sufficient time to slow down and let the other vehicle pass in front of you.
If you are that close that rapidly slowing down doesn't help, your reaction time plus the relatively slow rate of acceleration means that speeding up won't help either.
Cars can slow down much, much faster than they can speed up. Look at any 0-60 and 60-0 times in car reviews.
If there is any situation when you can see a potential accident and speeding up "saves you", then you also have sufficient time to slow down and let the other vehicle pass in front of you.
If you are that close that rapidly slowing down doesn't help, your reaction time plus the relatively slow rate of acceleration means that speeding up won't help either.
(Disclaimer: this doesn't work with trains.)