At only $200, it’s very difficult to find a capable fast action camera, much less one that fits into an ultracompact body. There are only a handful of ultracompact candidates that come close to having the long zoom range needed for fast action photographs, but even these cameras fail miserably in other aspects of performance - both the Casio V7 and Olympus FE240 have below average high ISO ability which makes fast action photos extremely noisy, and unusably in low-light situations.

The best choice in this class is the Casio V7 - despite its poor high ISO performance it has an adequate zoom range and fairly low shutter lag. The camera will only be usable in good daylight situations, however - it simply will not produce usable fast action photographs indoors or at night, and if you had planned to shoot anything but slow-moving daylight action, you’ll need to either increase your budget or put up with a larger camera.