The impact of nanoparticles (NPs) composed of atoms with covalent bonding is investigated numerically and theoretically. We use recent models of covalent bonding of carbon atoms and elaborate a numerical model of amorphous carbon (a-C) NPs, which may be applied for modeling soot particles. We compute the elastic moduli of the a-C material which agree well with the available data. We reveal an interesting phenomenon - stress-dependent adhesion, which refers to stress-enhanced formation of covalent bonds between contacting surfaces. We observe that the effective adhesion coefficient linearly depends on the maximal stress between the surfaces and explain this dependence. We compute the normal restitution coefficient for colliding NPs and explore the dependence of the critical velocity, demarcating bouncing and aggregative collisions, on the NP radius. Using the obtained elastic and stress-dependent adhesive coefficients we develop a theory for the critical velocity. The predictions of the theory agree very well with the simulation results.