Making something opereated by velocity is difficult because it needs to measure the relative velocity of surrounding objects or whatever you consider your reference frame. For example, a GPS can do this because it determines its position relative to the earth periodically and can therefore calculate velocity.
It is much easier to measure accelleration, because that can be done from inside a inertial reference frame. Note however that the force of gravity then can't be distinguished from accelleration due to change in velocity.
There small electronic chips that can measure accelleration and report it either via a voltage or digitally. This, with some firmware, can be used to detect specific gestures like you describe. Just like there are small electronic accellerometers, there are also small electronic gyrsoscopes. These report the angular velocity instead of angular position like mechanical gyroscopes do. These small gryros and accellorometers together are used in various motion and gesture detection schemes, like the wii toy, for example.
There are also very basic motion sensors. These look like a switch electrically that randomly opens and closes as a result of motion, and freezes state when stationary. They detect motion only, and are not useful for detecting specific gestures or determining velocity.