It occurred to me while driving to the dentist that there is
a phenomenon I really don't understand. I decided that it
might involve jerk (no, not me). What do you guys think?
If my car is in neutral and I roll slowly up a slight grade I
eventually reverse my direction and roll back down. The
turnaround is very smooth; I feel no sudden discontinuity. I
have tried to apply my brake at the instant of the turnaround
many times in this situation, and whenever I do I feel a
discontinuity in the motion. I'm convinced that I've hit the
instant dead on more than once, but still the discontinuity
is always present, and not noticeably varying in magnitude.
What's happening here? There is no discontinuity in velocity,
but when I apply the brake there is a discontinuity in the
acceleration. Of course the car is in equilibrium in an
accelerated frame while it slows, but I can't believe that is
the cause (the rapid change to a nonaccelerating frame)
because the acceleration can vary a great deal and the
subjective discontinuity does not seem to do so.