Image sequences allow visualizing dynamic systems and understanding their intrinsic characteristics. One first component of this dynamics is retrieved from the estimation of the velocity displayed on the sequence. Motion estimation has been extensively studied in the literature of image processing and computer vision. In this paper, we step beyond the traditional optical flow methods and address the problem of recovering the acceleration from the whole temporal sequence. This issue has been poorly investigated, even if this is of major importance for major data types, such as fluid flow images. Acceleration is defined as the space-time function resulting from the forces applied to the studied system. To estimate its value, we propose a variational approach where an energy function is designed to model both the motion and the acceleration fields. The contributions of the paper are twofold: first, we introduce a unified variational formulation of motion and acceleration under space-time constraints; second, we describe the minimization scheme, which allows retrieving the estimations, and provide the full information on the discretization schemes. Last, experiments illustrate the potentiality of the method on synthetic and real image sequences, visualizing fluid-like flows, where direct and precise calculation of acceleration is of primary importance.