Polymerization of actin filaments is the primary source of motility in lamellipodia and it is controlled by a variety of regulatory proteins. The underlying molecular mechanisms are only partially understood and a precise determination of dynamical properties of force generation is necessary. By using optical tweezers we have measured with millisecond (ms) temporal resolution and picoNewton (pN) sensitivity the force-velocity (Fv) relationship and the power dissipated by lamellipodia of dorsal root ganglia (DRG) neurons. When force and velocity are averaged over 3-5 s, the Fv relationships can be flat. On a finer time scale, random occurrence of fast growths and sub-second retractions become predominant. Maximal power dissipated by lamellipodia over a silica bead with a diameter of 1 m is 10-16 W. Our results clarify the dynamical properties of force generation: i - force generation is a probabilistic process; ii - underlying biological events have a bandwidth up to at least 10 Hz; iii - fast growths of lamellipodia leading edge alternate with local retractions.