Supernova remnants (SNRs) are among the most important targets for γ-ray observatories. Being prominent non-thermal sources, they are very likely responsible for the acceleration of the bulk of Galactic cosmic rays (CRs). To firmly establish the SNR paradigm for the origin of cosmic rays, it should be confirmed that protons are indeed accelerated in, and released from, SNRs with the appropriate flux and spectrum. This can be done by detailed theoretical models which account for microphysics of acceleration and various radiation processes of hadrons and leptons. The current generation of Cherenkov telescopes has insufficient sensitivity to constrain theoretical models. A new facility, the Cherenkov Telescope Array (CTA), will have superior capabilities and may finally resolve this long standing issue of high-energy astrophysics. We want to assess the capabilities of CTA to reveal the physics of various types of SNRs in the initial 2000 years of their evolution. During this time, the efficiency to accelerate cosmic rays is highest. We perform time-dependent simulations of the hydrodynamics, the magnetic fields, the cosmic-ray acceleration, and the non-thermal emission for type Ia, Ic and IIP SNRs. We calculate the CTA response to the γ-ray emission from these SNRs for various ages and distances, and we perform a realistic analysis of the simulated data. We derive distance limits for the detectability and resolvability of these SNR types at several ages. We test the ability of CTA to reconstruct their morphological and spectral parameters as a function of their distance. Finally, we estimate how well CTA data will constrain the theoretical models.
