If $a(t)$ denotes the acceleration of an object, then $a^\prime(t)$ represents the jerk.
I'm looking for an intuitive explanation of this phenomena. I'm hoping the following anecdote provides the intuition of how one might experience / explain jerk.
Suppose you're driving your car, and you approach a stoplight. The car then has a non-constant change in acceleration, $a'(t).$ Now, the moment the car comes to a full stop, we experience the car rocking back and forth. This is because the acceleration $a(t)$ goes to zero, but the change in acceleration at that time $a'(t)$ is . . .
Now, I would attempt to finish the explanation, but I lack the requisite language. My intuition is that $a'(t)$ is large, infinite, or is best approximated by an impulse function as $a(t)$ gets close to $0$. I'm not assuming that $a'(t)$ is differentiable, nor am I assuming it is even continuous.
Is this the right intuition? Would one of you be willing to provide another anecdote that one might experience on a day to day basis?