# Finding an equation to represent a jerk

1. Aug 15, 2009

### hover

hey everyone,
The title of this thread explains what I'm trying to do. I want to find an equation that can represent a jerk. A jerk is a change in acceleration with respect to time. What I really want though is an equation for a jerk that doesn't have a time variable in it. I think I know the answer but I want people to back up my answer so here we go.

We know that this is true
$$j=j$$

A jerk is equal to a jerk.... this really doesn't tell us anything about a jerk. So we now integrate by dt and we get
$$\int jdt= jt+C_1$$

The units of this equation are equal to an acceleration so this equation must be this
$$jt+a_i=a_f$$

Of course, we can keep integrating till we get down to distances so i'll show those now without doing the work.
$$\frac{jt^2}{2}+a_it+v_i=v_f$$
$$\frac{jt^3}{6}+\frac{a_it^2}{2}+v_it=d$$

Ok so now I have three equations that I could at least try solving for a jerk but there is a problem. All these equations involve time. The next logical thing that I can do is to substitute "t" into an equation, but first I need an equation to solve for time. I'll use the first equation.
$$jt+a_i=a_f$$
$$jt=a_f-a_i$$
$$t=\frac{a_f-a_i}{j}$$

Now I'll substitute that into the second equation.
$$\frac{jt^2}{2}+a_it+v_i=v_f$$
$$\frac{j(a_f-a_i)^2}{2j^2}+\frac{a_i(a_f-a_i)}{j}+v_i=v_f$$
then I simplify and try to get j on one side
$$\frac{a_f^2-2a_fa_i+a_i^2}{2j}+\frac{a_fa_i-a_i^2}{j}+v_i=v_f$$
$$\frac{a_f^2-2a_fa_i+a_i^2}{2j}+\frac{a_fa_i-a_i^2}{j}=v_f-v_i$$
$$\frac{a_f^2-2a_fa_i+a_i^2}{2j}+\frac{2a_fa_i-2a_i^2}{2j}=v_f-v_i$$
$$\frac{a_f^2-2a_fa_i+a_i^2+2a_fa_i-2a_i^2}{2j}=v_f-v_i$$
$$\frac{a_f^2-a_i^2}{2j}=v_f-v_i$$
$$\frac{a_f^2-a_i^2}{v_f-v_i}=2j$$
$$\frac{a_f^2-a_i^2}{2(v_f-v_i)}=j$$

So the final equation I get is this
$$j=\frac{a_f^2-a_i^2}{2(v_f-v_i)}$$

but is this right? Lets check the units. On top we have meters^2 per second^4 and on the bottom we have meters per second
$$\frac {m^2}{s^4}* \frac{s}{m}= \frac {m}{s^3}$$

Well at least the units are right but is this equation right?

Thanks for helping me out!!

2. Aug 15, 2009

### drizzle

looks fine, is jerk stands for the word jerk I know or am I missing something here?
why would you need an equation to represent a jerk

3. Aug 15, 2009

### hover

I was just extremely curious. I've been wanting to know an equation for a jerk for awhile now. What fueled my curiosity even more was the extreme lack of equations for a jerk. I have been searching everywhere for an equation that can represent a jerk. From my old physics book from high school and on the internet. I could never find an equation.

4. Aug 15, 2009

### DrGreg

In physics, "jerk" means "rate of change of acceleration", in the same way that "acceleration" means "rate of change of velocity" and "velocity" means "rate of change of distance".

5. Aug 15, 2009

### DrGreg

To be honest, I haven't checked whether your equation is right or not. It sounds plausible. The reason you haven't found an equation is the books is because you are assuming the jerk remains constant over time. In the real world, that's unlikely to be true, so your equation isn't really of much practical use. (In my view.)

6. Aug 15, 2009

### drizzle

I see, he did mention that in his post

7. Aug 15, 2009

### Creator

Could someone tell me why all the latex equations used in , say the first post, come out BLACK....cannot read them....maybe my Computer Settings ??

8. Aug 15, 2009

### ideasrule

That equation's right because a common kinematic equation is Vf2-Vi2=2ad. For jerk, velocity corresponds to distance, acceleration to velocity, and jerk to acceleration, so the equation for jerk should logically be Af2-Ai2=2jv

9. Aug 16, 2009

### gmax137

take a look at the thread "why is the math output hard to read sometimes" in the forum feedback section. I bet you're using internet explorer 6...

10. Aug 16, 2009

### DrGreg

You are probably using Internet Explorer v6 or some earlier version. If you are allowed to install software on the computer you use, you should upgrade to either a later version of Internet Explorer, or some other browser such as Firefox or Safari. There was a discussion about this towards the end of this thread (post #63 onwards). If you can't install software, all you can do is click on each equation to see the LaTeX that was used to create it.

Oops...gmax137 beat me to it!

11. Jan 3, 2010

### danielatha4

Xf=Xo+Vot+1/2aot2+1/6Jt3

af2=ao2+2J(Vf-Vo)

I'm not 100% on that second one