New vibration after braking hard

Sticking brake caliper. To verify this, stop on a slight incline, shift to neutral, release the brakes, then see if the vehicle creeps downhill on its own. If it does not, you can figure out which brake is causing the problem by observing which wheel is hot after a short drive. Next, stop on that incline again, place a block about a foot downhill of one tire, then crawl underneath and open the bleeder screw on that caliper. If the brake releases, suspect that rubber flex hose is constricted. If it does not release, suspect the caliper, especially if those brake pads were replaced previously. Often, as the pads wear and the piston works its way out of the caliper housing to self-adjust, a ring of dirt or rust forms on the piston. If that piston is able to be pressed back in far enough to make room for the new pads, as those wear and the piston self-adjusts out again, it binds when that ring gets stuck under the internal seal. We used to always rebuild calipers as part of a normal brake job in the 1980's, but today professionally-rebuilt calipers are rather inexpensive, so we just replace them.