With the advent of advanced testing strategies like laser-induced particle impact test, it is possible to study materials mechanics under extremely high deformation rates, i.e., above 10^6 s^-1, a relatively less explored regime of strain rates. In this study, we accelerate microparticles of commercially pure titanium to ~100 m/s towards a rigid substrate and record their deformation upon impact in real time. We also conduct finite element modeling of the experimentally recorded impacts using two constitutive equations: Johnson-Cook and Zerilli-Armstrong. We show that titanium microparticles experience strain rates in the range of 10^6-10^10 s^-1 upon impact. We evaluate the capability of the Johnson-Cook and Zerilli-Armstrong equations in predicting material response at ultra-high strain rates. With an optimization-based constitutive modeling approach, we also propose updated strain rate-related constitutive parameters for both equations that can improve the extent to which they can successfully describe the deformation of materials at higher strain rates.