I am curious about the validity of (re)phrasing of Newton’s 2nd Law as “instantaneous.” The acceleration is non-differentiable at T=0. Can we really combine it

I am curious about the validity of (re)phrasing of Newton’s 2nd Law as “instantaneous.” The acceleration is non-differentiable at T=0. Can we really combine it with analysis of times t<T and t>T?