Computed tomography has emerged as the method of choice for scanning complex shapes as well as interior structures of stationary objects. Recent progress has also allowed the use of CT for analyzing deforming objects and dynamic phenomena, although the deformations have been constrained to be either slow or periodic motions. In this work we improve the tomographic reconstruction of time-varying geometries undergoing faster, non-periodic deformations. Our method uses a warp-and-project approach that allows us to introduce an essentially continuous time axis where consistency of the reconstructed shape with the projection images is enforced for the specific time and deformation state at which the image was captured. The method uses an efficient, time-adaptive solver that yields both the moving geometry as well as the deformation field. We validate our method with extensive experiments using both synthetic and real data from a range of different application scenarios.