My 1994 Ford Taurus with auto transmission and 162000 and a 3.8L engine occasionally thumps when I use the brakes to stop and when I release the brakes after they thump stopping will thump again. I did notice low brake fluid level.
Check the condition of the rotors, pay attention to pitted and rusted areas on the inner and outer surfaces. If low on fluid, it means it's time to replace at least the front, and possibly the rear brakes! Inspect all 4 wheels!