Yes, during big lead falls and similar situations it feels like either time stops or the brain is in the overdrive. None is actually true. Unfortunately, we (most of us at least) can’t control time and even can’t speed up brain processes. But we remember past events differently; it makes sense to remember critical life threatening events well, it can save you in future and hence improve chances to survive. So our brain knows when to save event memories with a lot of details (running from a tiger) and when with very few (fishing with a line).
The regions described as amygdala is some structures with distinct connectional and functional characteristics of the brain in complex vertebrates, including humans. It is believed that amygdala gives emotions to the memories, colours memories, so we end up with happy and sad recollections.
We feel that “time stopped” just because our memory “tape” has tons of emotionally coloured bits of information per unit of time.