I agree that you have a good case if you choose to contest the ticket - it's one of the most bogus tickets I've seen posted on here... It even appears the officer reflexively wrote (a) due to writing 22349(a) over and over for the last 10 years or so...
The fastest and easiest way out is to just take traffic school - the total cash outlay will run about $250-$300.
The biggest downside to fighting the ticket is that it is your first ticket, and you will have to invest a substantial amount of time and energy into studying the relevant law and court procedure/custom before you are able to prepare a legally sound defense for the charge against you. This sort of upfront investment pays off fast when you average 2-3 tickets per year like me, but not if you don't expect to get another ticket in the next 20 years.
As for your case, you shouldn't have too much trouble convincing the judge that 10mph was safe and reasonable considering that you didn't strike the vehicle in front of you. Sure hard braking was necessary, but that's normal when the driver in front if you slams on the brakes for no good reason. You could also use the officer to buttress your version by asking the officer if it's normal for some drivers to reflexively slam on the brakes when they spot a police car (YES!). Of course you will also testify to your clean record and no accidents for the last 20 years as evidence of your good judgment while driving.
There is always the possibility of losing the case and getting a point on your license if the judge happens to be an even bigger ignoramus than the idiot CHP who wrote the ticket, but unfortunately that's the reality of many traffic court (small town judges being particularly notorious for that).

