# Why is jerk the change in acceleration over time?

1. Apr 10, 2012

### Mahkoe

Recently I found out about jerk (or jolt). I've found that it represents the change in acceleration over time. To me, this makes no sense at all. To me, the change in acceleration is directly related to the radial distance between the two objects (if the forces acting on or imaginary objects are due to gravity), and has nothing to do with time. I don't get why the fact that jerk is measured in change in acceleration over time will give the correct results if we for example, throw a 20g ball directly upwards from a 20kg planet whose radius is say, 100m, at two different speeds. The faster initial velocity will cause the ball to travel higher, therefore the change in acceleration being greater, and although yes the change in time will be greater, I just can't grasp why it works and how the change in acceleration is related to the change in time. Could someone please explain what is going on and why, or maybe point a very digestible tutorial, and try to avoid calculus if possible. Thank you very much

2. Apr 10, 2012

### genericusrnme

But that radial distance between two objects changes with time, so by extention so does the acceleration and alas acceleration can be written as a function of time.

3. Apr 10, 2012

### Mahkoe

But here's the thing; when the initial velocity is faster, the radial distance will change more with time. You're probably right, but I really don't understand

4. Apr 10, 2012

### genericusrnme

Yes, if the radial distance changes more with time then the acceleration also changes more with time, since as you say, acceleration is directly related to the radial distance.

If you were to use calculus this is the equivelant of saying simply that j(t)=a'(t) where j(t) is the jerk as a function of time and a(t) is the acceleration as a function of time.

5. Apr 10, 2012

### Mahkoe

You've just said that if the initial velocity is greater, the acceleration will change more with time, meaning the jerk is greater. Maybe I was never told that jerk is not something constant, that it is found with the initial vertical velocity?

6. Apr 10, 2012

### Nabeshin

I don't understand, Jerk is DEFINED to be the third time derivative of position, or the first time derivative of the acceleration. That's all there is to it...

7. Apr 10, 2012

### Mahkoe

Sorry to be the freak here, but "That's all there is to it" is not good enough for me

Last edited: Apr 10, 2012
8. Apr 10, 2012

### DaveC426913

Change in position is velocity.
Change in velocity is acceleration.
Change in acceleration is jerk.

A common example of jerk acceleration is a rocket that burns fuel, thus decreasing it mass, thus (due to a=F/m) causing a steady increase in the rate of acceleration over time.

In your example of tossing a ball, you've missed one critical component:

For a low altitude throw, the acceleration is indeed constant (9.8m/s2 on Earth) - thus no jerk.

But for very big distances on your tiny planet (or, on Earth a high altitude throw of many miles) gravity drops off noticeably. Thus, the acceleration is not constant. The rate of acceleration decreases over time (9.8m/s2 at the start, but < 9.8m/s2 at the top of the arc).

Last edited: Apr 10, 2012
9. Apr 10, 2012

### AlephZero

I think most of your problem is that you picked a bad example to understand the idea. The fact that in your example you can write the acceleration as a simple function of distance isn't relevant to the idea of what "jerk" is.

Think about a different example, like a car accelerating from rest and then driving at the speed limit. Suppose the initial acceleration was 2 m/s2. When the speed is near the speed limit, the driver lifts his foot off the gas so the acceleration drops to zero (i.e. the car continues driving at constant speed) in say 0.5 seconds.

The acceleration has changed from 2 to 0 in 0.5 sec. So the jerk or jolt is (0-2) / 0.5 = -4 m/s3.

That's "all there is to it".

10. Apr 10, 2012

### Mahkoe

Okay, I understand now. But then, how is jolt used in the example of the ball on the 20kg planet? How do you calculate the jolt, and is it the same for every altitude and initial velocity? Thanks for all the help, btw

Last edited: Apr 10, 2012
11. Apr 11, 2012

### genericusrnme

Working with the 1/r potential is kinda tricky if we want exact answers

Let's use a simple example of the harmonic oscillator.
We can solve the equations of motion to get x(t)=Cos(t) (if we use units such that all the coefficients like mass, spring constant etc = 1)

In this case the acceleration is x''(t)=-Cos(t)

Why is this?
Because the definition of the harmonic oscillator is one where the force is equal to minus the displacment from the origin.

As we can see, this function changes with time. If we were to calculate the change of x''(t) with respect to time we would get the function x'''(t)=Sin(t)
This is so because at t=n pi the displacment is at a maximum (Cos(n pi)= ±1) and so the force is also at a maximum which means that the rate of change of the force is zero (Sin(n pi)=0).

If we change the initial conditions we get the solution x(t)=a Cos(t+b), changing the initial velocity gives us the a and changing the initial position gives us the b. If we use this new x(t) we arrive at the jolt as x'''(t)=a Sin(t+b), so the jolt as a function of time does indeed change given different initial conditions.

12. Apr 11, 2012

### AlephZero

As the wikipedia page http://en.wikipedia.org/wiki/Jerk_(physics [Broken]) says, it probably isn't used in practice in that situation, because it doesn't tell you anything interesting.

If you can define acceleration easily as a function of position, you could find the jerk by using the chain rule:
$$\frac{da}{dt} = \frac {da}{dx}\frac{dx}{dt} = v \frac{da}{dx}$$
(you said you preferred avoiding calculus, but that's not always possible). That shows it is not indepedent of the velocity. You can understand that without calcuus, because when the ball is at the top of its flight and the velocity is zero, the acceleration is not changing so the jerk is also zero. But it the ball was at the same height and moving with a high velocity, its acceleration would be changing and the jerk would not be zero.

Jerk or jolt is only used where it represents something physically important to what is being designed or analysed, like starting or stopping of a vehicle or an elevator, etc.

Last edited by a moderator: May 5, 2017
13. Apr 11, 2012

### Creator

There are many engineering applications for jerk... from design of auto air bags to roller coasters to ejection seats.

You can see from the eqn. that jerk can be increased by an increase in acceleration or by decrease in the time span for the change.

Also, (briefly mentioned in Wiki) jerk involves a change in force per unit time (dF/dt) when mass is involved...and is sometimes referred to as "yank"... :)
dF/dt = m(dA/dt)

Creator

Oh, yea, don't forget about "jounce" which is the rate of change of jerk with time. :)
Fourth time derivative of position.
...

Last edited: Apr 11, 2012
14. Apr 11, 2012

### rbj

what's there to make sense or nonsense? it's just a definition. what you're saying here makes little sense to me.

objects in free fall experience no jerk and, from the POV or general relativity, don't even experience acceleration that can be measured in their own frame of reference.

i dunno if you have ever ridden a subway train. sometimes there are no seats and you have to stand. there were even times i had to stand and could not even reach a strap or bar to stabilize my stand. when the train accelerates or decelerates at a constant rate (the jerk is zero), then i can adjust the angle of my standing and i need no strap to hang on to. it's just like standing on a slightly sloping incline (and a slight increase in the apparent gravity). but as soon as that acceleration changed, the risk of me bumping into someone else or falling over was greater. that is what jerk is all about.

sitting in a chair or standing on the floor is indistinguishable from a constant acceleration (where the jerk is zero). but even in general relativity, jerk is absolute. doesn't matter where you are, everyone will experience an equal amount of jerk equally.

15. Apr 11, 2012

### DaveC426913

Thing is, it's not like jerk really is about jerks and jolts. I listed several examples of smooth, continuous and long-duration jerks.