From your username it sounds like you're from Illinois. I am unsure sure about all of Illinois's Board of Nursing Policies, and from your description it appears that you were most likely charged with a reckless or careless driving. However, I don't know if you pled guilty to a lesser offense like I did, or to the reckless driving, if that's what you were charged with.
From my personal experience, I would say you're completely fine. Especially if this is you're one and only incident with no alcohol or drugs involved. For Michigan, my home state, I didn't have to send in any court documents. I only had to submit an explanation of my prior arrests, and I got licensed no problem.
For Texas, I didn't have to state my most recent incident because it was dropped, but for Louisiana I had to because they include dropped/expunged records. So, when I called the Louisiana BON and they said the recommended plan of action was to suspend my license for 5 years, I IMMEDIATELY withdrew my application. I could have fought it, but like I said in my original post I would have been placed on probation and that would have been difficult to find a job, or worse my license could have been flat out denied. So where I'm getting at is that my advice would be to SUBMIT all the court documents and explanation of events, wait a week then call them back, and if you hear from them anything along the lines of "We are NOT going to license you...", "You're license is going to be revoked...", and etc....WITHDRAW your application immediately and apply to another state. BUT...and this is a BIG BUTTTTT, I highly doubt that will happen to you, like it did with me. Just be persistent, follow up with the BON, and be honest. If you don't need to include expunged or dropped charges, DON'T INCLUDE IT! However, it sounds like this incident may be on your record. ALSO, I would recommend running a background check on yourself, an FBI background check through livescan. This will for sure let you know what's on your record. Bottom line: just be persistent, follow up with the BON, and don't speed lol. Also, compared to me you're a saint, so my gut feeling is telling me you're completely fine after you submit the required documents:) Let me know if you have any questions!