Here is the way I understand "jerk".
Say I am on a commuter train, standing up, as the train comes into the
station. As it slows to a stop, it has an approximately constant
acceleration opposite the direction of motion. Once it comes to a stop,
of course it doesn't reverse direction but it stays stopped. In other
words, when the velocity reaches zero, the acceleration also
decreases to zero. That's the "jerk", and I think it's the same thing
that happens to Leigh's car--the only difference being the source of
the net force causing the acceleration (with the car coasting uphill,
the force before the car stops is gravity, the force after, or when, the
car stops is gravity plus brakes. With the train, the force causing it
to slow to a stop ceases when the train stops; I guess it's kinetic
friction).
Now why do I FEEL the "jerk"? I feel it because while acceleration is
not zero I must lean in such a way as to avoid falling over. Then if
the acceleration goes to zero, I must quickly change my position or I
fall over anyway.
I think "jerk" is important only to a being (or machine?) which is able
to compensate somehow for being in a noninertial frame. When the
acceleration changes, the compensation must also change.
--
Martha Takats