Pushing down on the gas pedal of a car a good example of jerk?
I'm trying to think of the clearest examples to demonstrate the concept of jerk to a layman.

Pushing down the gas pedal is not a good example of jerk.

A car with constant acceleration (zero jerk) would mean holding the gas pedal down at a constant displacement/angle from its starting point i.e. my foot is keeping the gas pedal held down, halfway constantly.

The answer is no (in an idealized case).

If you hold the gas pedal down at a constant angle then you inject a constant amount, $k*q_0$, of energy (mass of fuel per second multiplied with conversion constant $k$) in the car and in consequence the kinetic energy of the automobile at any moment of time, *t*, must be always equal to the total energy injected up to that moment *t*. Mathematically this can be written like this:

As you can see the solution is not a constant acceleration.

A car with ... an increasing acceleration would mean gradually pushing down the gas pedal so its displacement/angle is increasing from its starting point at a constant rate.

Again no.

If you press the pedal more and more as the time passes, at each moment you inject $q(t) = q_0*k*b*t$ where $b$ is a constant that depends on how fast you push the pedal. In consequence:

This time you get a constant acceleration.

## Best Answer

Consider the force exerted by a spring on an object: $$\vec{F}=-k\vec{X},$$ where $\vec{X}$ is the deflection of the spring from its self-equilibrium. Calculate the time rate of change of the spring force:$$\frac{d\vec{F}}{dt}=-k\frac{d\vec{X}}{dt}.$$

Is the deflection changing is the spring is oscillating? Yes. So the time rate of change of the force exists. Now the real question is "Is the time rate of change of force useful for analysis in physics (as opposed to engineering/comfort/etc.)?" Generally, no. Hamiltonian mechanics answers this question in that only the first derivatives of position and momentum, along with constraints, are sufficient to describe the motions of systems.

Other responders may expand on this idea.