# Real world intuitive explanation of Jerk

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?

• An electric shuttle bus at an airport is a great demonstration of jerk and all bus drivers there are jerk experts. – safesphere Oct 10 '18 at 19:37

$$m\ddot x = F,$$ then, $$m\dddot x = \dot F.$$