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- Vehicle Speed: ##v = \frac{dx}{dt}##
- Vehicle Distance: ##x##
- Vehicle Speed after Deceleration: ##v - Δv = \frac{dx}{dt} - \frac{Δx}{Δt}## (Is there perhaps a different way of writing this that's more useful? Not sure why but I feel like there is. Probably not.)
- Lag/Reaction Time: ##t##

That aside, does anyone have any ideas for how I can start to model what I'm trying to model? I've also created a simple graphic that might be helpful, you can ignore the subscript on the vehicle distance variable.

I feel like I might just be lacking the initial intuition, as might be obvious by the jumbled manner in which I've put this post together. If anyone can give me any suggestions on creating this initial model I'd appreciate it!