The real answer here is it depends a great deal on the GPS itself, then it depends on how whatever software is reporting and logging this information post processes it.
GPS itself is capable of reporting an instantaneous velocity vector calculated by measuring the doppler shift from each satellite. (Comes in as a GPVTG sentence in the NMEA data) So if the receiver is tracking a lot of satellites with a good distribution and there isnt a lot of multipath problems, the accuracy of this vector is ridiculously good. Also, a receiver may not support GPVTG.
Now you can also get velocity data from a GPRMC (ie normal position data) sentence too. According to the specification, the bearing here is supposed to be calculated based on position track angle (presumably so that you dont have to be moving to have a GPS bearing).. The spec seems silent to the origin of the speed reported in this sentence -- seems like it could be calculated as track speed (average speed over the interval) but could easily be reported as instantaneous speed as well.
Of course I haven't tested any, but I imagine in practice, GPS receivers would normally report track/position averaged data in GPRMC and instantaneous data in GPVTG. Any software that is supposed to present this data to a user would have to determine how to aggregate and filter it to provide for its intended purpose. If you really intend to beat a speeding ticket with GPS I would suggest that you need data points of either type (instantaneous or averaged) with at least 1Hz if not 5Hz granularity along with knowledge of what the data represents and how the raw data is filtered and processed. This 30s interval business in this case is just dumb, and nobody ever bothered to determine anything about the nature of the data it seems.