  Let X be an open subset of R^2. We study the dynamic operator, A, integrating
over a family of level curves in X when the object changes between the
measurement. We use analytic microlocal analysis to determine which
singularities can be recovered by the data-set. Our results show that not all
singularities can be recovered, as the object moves with a speed lower than the
X-ray source. We establish stability estimates and prove that the injectivity
and stability are of a generic set if the dynamic operator satisfies the
visibility, no conjugate points, and local Bolker conditions. We also show this
results can be implemented to Fan beam geometry.
