Following too closely is a function of driver reaction time for safety, not merely distance. It takes about 2.7 seconds for the human brain to react to act, for brakes etc.... So your speed will determine how far the car might travel in that matter of seconds.
I hope this observation helps as you attempt to articulate a defense.
Generally, the prosecutor can amend the ticket to a non-moving violation provided you are eligible. The cost of the ticket will increase as the non-moving violation is not reported to your driving record. You can also schedule the matter for a trial to determine guilt. The Court may grant a continuance to hire counsel or to give you more time to review it. If discovery exists, then you can request it at any time, as most jursidictions around Lawrence have open file policies. Traffic tickets do not always have any discovery beyond the physical ticket, but it varies and should be explored.
An attorney would be able to review the ticket and advise you on the specifics of the court as it varies. The procedures are different in the City of Lawrence when compared to the District Court. An attorney would also be able to speak with you regarding the consequences of trial, the specific costs of an amendment and your options.
Disclaimer - This does not constitute legal advice and does not create an attorney-client relationship.