Tell your dad, because you're probably going to want to hire a traffic ticket lawyer, to see if they can try and get the cop to bring it down to a lower violation (because careless driving is a pretty serious traffic ticket, usually lots of points on record possibly even could get license suspended even) so definitely should tell your dad, and explain what happened, and see if you can get a lawyer. As an experienced lawyer may be able to get it dismissed, as sometimes if its a first time offense, they may let you agree to take traffic school and pay a smaller fine along with a dismissal, for purposes that it doesn't give you a point on your record for insurance, etc. However, usually, at least where I live, they don't offer that if it is careless or reckless driving, but depends on where you are. And so hence, why should talk to a lawyer about it. Look for somebody with lots of experience, as they may have knowledge of what to best do in your situation, and what your options are, so you aren't totally effed.
How did he gauge your speed by the way? Did you ever find that out? Because some of those methods aren't the most reliable and if 90 is careless driving, but 89 would just be a speeding ticket, that's a pretty big deal, especially if it could mean the difference between having the opportunity to get a dismissal if you agree to pay a small fine and take traffic school for a first time offense, and not being able to have that option. So better get a lawyer or something who knows how to best address your situation.
Sometimes the cop doesn't show up. But I bet he will since its careless driving. I once got a ticket for some stupid thing like passing on a double yellow line, and then after he pulled me over for it, and I had to show him my license registration and insurance, I accidentally gave him one of my old insurance cards, as I never took it out from my glove box and I just got new cards, and I must have grabbed the wrong one. So when he came back and said that, I then frantically am digging for the other one, and right as I found it, and tried to give him my new card, he just said, "too late, I already wrote the ticket." The ticket was super high. That was messed up, but was just a "fix it ticket anyways" But I was like, what an effing ******! Cop then never showed up for court. So got my double line passing one dismissed too.