We develop a method for obtaining exact time-dependent solutions in Jackiw-Teitelboim gravity coupled to nonconformal matter and study consequences for NAdS2 holography. We study holographic quenches in which we find that the black hole mass increases. A semiholographic model composed of an infrared NAdS2 holographic sector representing the mutual strong interactions of trapped impurities confined at a spatial point is proposed. The holographic sector couples to the position of a displaced impurity acting as a self-consistent boundary source. This effective 0+1-dimensional description has a total conserved energy. Irrespective of the initial velocity of the particle, the black hole mass initially increases, but after the horizon runs away to infinity in the physical patch, the mass vanishes in the long run. The total energy is completely transferred to the kinetic energy or the self-consistent confining potential energy of the impurity. For initial velocities below a critical value determined by the mutual coupling, the black hole mass changes sign in finite time. Above this critical velocity, the initial condition of the particle can be retrieved from the SL(2,R) invariant exponent that governs the exponential growth of the bulk gravitational SL(2,R) charges at late time. © 2020 authors. Published by the American Physical Society.