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The distribution of elements produced in the inner-most layers of a supernova explosion is a key diagnostic for studying the collapse of massive stars. Here we present the results of a 2.4 Ms \textit{NuSTAR} observing campaign aimed at studying the supernova remnant Cassiopeia A (Cas A). We perform spatially-resolved spectroscopic analyses of the $^{44}$Ti ejecta which we use to determine the Doppler shift and thus the three-dimensional (3D) velocities of the $^{44}$Ti ejecta. We find an initial $^{44}$Ti mass of 1.54 $\pm$ 0.21 $\times 10^{-4}$ M$_{\odot}$ which has a present day average momentum direction of 340$^{\circ}$ $\pm$ 15$^{\circ}$ projected on to the plane of the sky (measured clockwise from Celestial North) and tilted by 58$^{\circ}$ $\pm$ 20$^{\circ}$ into the plane of the sky away from the observer, roughly opposite to the inferred direction of motion of the central compact object. We find some $^{44}$Ti ejecta that are clearly interior to the reverse shock and some that are clearly exterior to the reverse shock. Where we observe $^{44}$Ti ejecta exterior to the reverse shock we also see shock-heated iron; however, there are regions where we see iron but do not observe $^{44}$Ti. This suggests that the local conditions of the supernova shock during explosive nucleosynthesis varied enough to suppress the production of $^{44}$Ti in some regions by at least a factor of two, even in regions that are assumed to be the result of processes like $\alpha$-rich freezeout that should produce both iron and titanium., Comment: 14 pages, 13 figures (6 3D animations in the online journal). Accepted for publication in ApJ