I would probably move your AF mode to AI Servo -- and then check your AF Point. I would brush up on your camera's manual (it provides you with a few details). AI Servo should continue to focus on your subject the whole time. Try to start with your subject in the middle of your frame (if your AF Point is the center) and press your shutter button halfway. Even if your subject moves from the center, your camera *should* maintain focus on it.
If you are feeling ambitious, I'd even try back-button focusing. (Once you get used to it, you may never go back.) Basically, it removes the focusing part away from the shutter button and onto a different button. You don't have to worry about your camera not taking a picture because it is trying to focus! If you want to know more about it, let me know!
My AF point is in the center... I have checked my manual.
I would like to know more. What is back button focusing?
"back button focusing" is assigning a button on the back of the camera, where the thumb of your right hand rests, to use as the focus button, instead of using the shutter release. Then when you want the camera to focus you press the button you assigned.
Can we see a sample problem shot?
The book for my T2i says AI Focus AF switches the AF mode from One-Shot AF to AI Servo AF automatically if the still subject starts moving. Once in AI Servo mode, the focus confirmation light will not light, but it might beep. You have to keep the focus point on the moving subject. This makes it sound like AI Focus is a good choice.
I am just an amateur when it comes to actions shots. The shots that have been successful for me have been where I have my Canon Xti set on AI Servo, center weighted metering and a fast shutter speed. I have shot birds in sports mode, but prefer to shoot in Tv (shutter priority) with a speed of about 1/1500 to 1/2500. I will adjust F stop depending on available light. My technique is to use manual focus, watch the pattern of subject movement for a bit to get a feel for distance and location. Then I manually focus the lens on the spot where I anticipate the subject to be when I take the shot. After that I wait until a subject enters the "shot" zone. From there, small adjustments in focus can be made. Obviously, I take a lot of shots that don't work out, but that is the beauty of digital. I do use also multiple shot mode and keep the shutter held down as I lead the subject a bit. Like I said, I am not pro on this subject so hopefully others who know better will help out.
If you want a more detailed version on back-button focusing, here is a link to an article directly on Canon's site. http://www.learn.usa.canon.com/resources/articles/2011/backbutton_a...
As far as getting the 'fast movement effect,' basically you use a slow enough shutter speed to blur the background and you physically pan the camera to follow your subject -- allowing for it to stay in focus. (And I imagine there are plenty of other people here who can explain this better than I just did!)