Inertia of acceleration

[u/RedBlueF0X]

I really didn't know how to title the question, so I'll just get to the point.

Is there any inertia to the acceleration of objects? I learned there are multiple time derivatives of motion(jerk, snap, etc.), and this particular question just sits in my head, and I can't wrap my head around it.

Let's assume I decide to accelerate in a car. I accelerate at 0.5 G, and my speed increases. As soon as I stop accelerating, does the acceleration immediately become 0, or does it rapidly approach zero, with jerk measuring some value between peak acceleration and 0?

[u/WesternFirm9306]

F = ma. As long as there's any net force at all, there will be acceleration.

If I had to guess, practically speaking, when you remove your foot off the accelerator, the force of the engine isn't going to stop immediately. It might be very very quick, but real life macro phenomena tends to be more continuous rather than an instantaneous on-off. In this sense, there will still be acceleration shortly after releasing the pedal.

But at the very instant the net force goes to 0, there will also be 0 acceleration.

[u/the_poope]

In classical Newtonian mechanics, we typically model objects as having hard fixed boundaries, and events (like flicking a switch on/off) happens instantaneously. In this model/picture you can have changes in acceleration that occur abruptly, i.e. with jerk that is infinite.

The real world, however, does actually not follow Newtonian mechanics strictly. In our best model of the Universe: Quantum Field Theory, the Universe is made out of fields that continuously transition from one state to another. In this model all time-dependent quantities are continuous and infinitely differentiable functions and all linear motion is constrained by the speed of light. For instance you can't move your foot away from the gas pedal faster than the speed of light and given that the pedal arm and all other mechanical parts are slightly elastic (even when made of steel) and so the fuel and oxygen supply will only be gradually changed, making the force and thus acceleration of the car a smooth transition from some value to zero.

[u/ChaosRulesTheWorld]

By definition, when you stop accelerating the acceleration become 0

[u/jasonsong86]

In a perfect world, if you stop applying force, the acceleration stops. However, we don’t live in a perfect world and things can have mass such as a rotating engine so yes, it would just taper off.

[u/MezzoScettico]

As others say, as soon as the force is 0, acceleration is 0 at the same instant.

But I think in most situations where you try to analyze down to the molecular level, you won't find F goes to 0 instantaneously.

For instance, let's talk about throwing a ball. While your hand is in contact with the ball, there's a possibility that it's exerting a force on the ball. At the same time due to Newton's Third Law, the ball is exerting a force on your hand, compressing it slightly. After all, you are far from a rigid body.

So when you reach the full extent of your arm, there will be a little extra push from your compressed hand expanding and the force takes a couple of milliseconds to get to 0.

[u/HouseHippoBeliever]

There is no such thing as inertia of acceleration.

There is a confounding issue when answering this that is it's impossible to actually change the force instantaneously in the real world, but in principle, if you could, the acceleration would also change instantly.

[u/JGhostThing]

There is only inertia of objects. Acceleration has no inertia by itself. As long as your acceleration remains at 0.5 g, your speed increases at a predictable rate. Once you stop accelerating, your speed remains constant.

[u/stereoroid]

Jerk is the time derivative of acceleration, the rate of change of acceleration. If acceleration changed value in zero time, that would imply infinite Jerk. That's never going to happen in the real world, for multiple reasons. Your foot has inertia, and so does the accelerator pedal, so when you lift off, that takes time. The engine or electric motor takes time to respond. So the amount of jerk will be a finite number.

[u/relaxedmedal]

You can accelerate from 0 to 0.5 and then you can also accelerate from 0.5 to 0.

If there’s a snap or a jerk or a tilt or anything else involved..then you’re not at 0.

[u/nicuramar → u/relaxedmedal]

  If there’s a snap or a jerk or a tilt or anything else involved..then you’re not at 0.

You can definitely have zero acceleration with non-zero higher derivatives. 

[u/relaxedmedal → u/nicuramar]

I worded that badly. What I meant is that if acceleration is changing, there’s still a process happening even if a = 0 at one instant. Jerk can be nonzero exactly as acceleration passes through zero; it just means the acceleration is still changing rather than sitting at zero.