The actual time taken for a physical process is called its natural
time.
Generally, it is safe to assume that performing an analysis in
the natural time for a quasi-static process will produce accurate static
results. After all, if the real-life event actually occurs in a natural time
scale in which velocities are zero at the conclusion, a dynamic analysis should
be able to capture the fact that the analysis has, in fact, achieved a steady
state. You can increase the loading rate so that the same physical event occurs
in less time as long as the solution remains nearly the same as the true static
solution and dynamic effects remain insignificant.