Doing a calculation every 100ms on Arduino is quite straightforward. In principle you either configure a hardware timer or you continuously check millis() to see if 100ms has elapsed since your last action.
Knowing the speed at the beginning of the second and knowing the acceleration you can calculate (guess) the speed at 100ms intervals until the beginning of the next second.
Can you also increase the frequency of data delivery by configuring you GPS receiver say using the equivalent of the ublox u-center?