Using a first-principles approach we calculate the electron-phonon couplings in graphene for the transverse and longitudinal acoustic phonons. Analytic forms of the coupling matrix elements valid in the long-wavelength limit are found to give an almost quantitative description of the first-principles matrix elements even at shorter wavelengths. Using the analytic forms of the coupling matrix elements, we study the acoustic phonon-limited carrier mobility and quasiparticle lifetime observable in photoemission spectroscopy for temperatures 0-200 K and high carrier densities of 1012-1013 cm-2. We find that the intrinsic effective acoustic deformation potential of graphene is Ξeff=6.8 eV and that the temperature dependence of the mobility μ~T-α in the Bloch-Gru¨neisen regime increases beyond an α=4 dependence even in the absence of screening when the true coupling matrix elements are considered. The α>4 temperature dependence of the mobility is found to originate in a similar temperature dependence of the relaxation time at the Fermi level. The large disagreement between our calculated deformation potential and those extracted from experimental measurements (18-29 eV) indicates that additional or modified acoustic phonon-scattering mechanisms are at play in experimental situations.