I feel your pain. I have a Nikon Coolpix. It is great for posed pictures. But I can't get it to take a decent action shot at all. All of my pictures from the Hobbit Lass's meets are just blurs. If anyone has any suggestions for stopping action, please let me know. No, I can't just run out and spend hundreds of dollars on another camera.
The bad thing, that might be causing your blurriness, is using the zoom to zoom in too much. Better for focus to take the picture in wider frame and crop it on your computer to bring the action in. Even when my horses are all the way across the pasture, I don't zoom more than 2X. Not with that zoom. And because of the delay... take LOTS of pictures and expect to throw out lots of them. It's just too hard to perfectly time something that's running to get the right moment in their stride. You just have to take lots and get lucky. But I took these pics with a Coolpix.