If we zoom in on a single electron absorbing the momentum of a single photon, it will accelerate “instantly”. The same goes for e.g. an unstable atomic nucleus that ”splits”.

At macroscopic scales, I’m not aware of exactly instantaneous acceleration, since you would need some time to “sync” the movement of each atom in the object. But some processes will of course look instantaneous at any given time scale.

Aren’t you describing infinite acceleration, or discontinuous velocity?

Voltages can change abruptly. Therefore, forces can change abruptly, and hence acceleration as well.

Imagine a multistage rocket and the changes in acceleration.

Figure 4-3 in https://www.ibiblio.org/apollo/Documents/lvfea-AS506-Apollo1... shows this for Apollo 11.

I imagine if you zoom in far enough on those points you have the acceleration continuously changing as pressure slowly builds in the engines over several microseconds.

I was thinking more of the instant you shut off engines and disconnect 130,000 kg of mass of stage one.

There is an interesting Δa/Δt while fuel is consumed and mass changes.

There are discontinuities to the graph when engines are shut down and stages decoupled.

That’s a legitimate question: over small enough time periods (as the bolts explode over a non-zero period of time), is it continuous or discontinuous?

Over a macro scale, it’s discontinuous, of course.

It's nature, it's continuous at small enough scales.

But, checkout Zeno's paradox for more on your philosophical questions