Here is a test series I did at my granddaughter's softball game today where I used AFC to shoot her running from third to home.
18 shots in 4 seconds, this equates to 4.5 FPS so the camera does slow down a bit to focus, I have it set to focus priority.
I used the lowly Tamron 70-300 which is a lens I like to take to the softball field as it is light and has good reach and is sharp @ f8 and works fine outdoors in good sun.
The settings were TAv, 70mm, f8, (ISO 800) 1/1000 and I had it set for spot focus.
I was pleasantly surprised that every shot is in focus on the entire series, as she coming straight at me for 90 feet in 4 seconds.
I down sized, then put all the shots in powerpoint to show the collection so the series displays here look muddy, but every shot looks in focus and sharp.
The last picture is one I picked from the middle of the series but they all look right on the money.
I did not process the pictures except to crop and resize for posting.
The Tamron is not the greatest lens but It gives decent results, and post processing improves the output quite a bit.
My impression is that the AF in the K-3 is very effective, and definitely an improvement over my previous K-5.