The dust tail of Main-Belt Asteroid P/2010 A2 (LINEAR) has been observed with several telescopes at the at the Observatorio del Roque de los Muchachos on La Palma, Spain. Application of an inverse dust tail Monte Carlo method to the images of the dust ejecta from the object implies a sustained activity over some eight months. The onset of the activity occurred in late March 2009, with a peak dust mass loss rate of about 5 kg/s in early June 2009, decreasing afterwards to 0.1 kg/s near perihelion in early December 2009. The total amount of dust released is estimated to be 5x10^7 kg, which represents about 0.3% of the nucleus mass. The nucleus diameter is D=220 +/- 40 m, assuming a bulk albedo of p=0.11, typical of a S-type asteroid. The event could have been triggered by a collision, but this cannot be decided from this dataset alone.