# Questions tagged [jerk]

Jerk is the third derivative of displacement with respect to time. It is also the derivative of acceleration with respect to time.

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### On the derivation of the jerk term in tensor notation

The jerk vector $\mathbf{J}(t)$ may be (element-wise) written as $$J^{i} = \frac{d A^{i}}{d t} + \Gamma^{i}_{jk} A^{j}V^{k}~~~~(*).$$ However, I can't correctly get the second term of the RHS above. ...
1 vote
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### Is SHM an example of a jerk?

So i was wondering if simple harmonic motion (SHM) is an example of a jerk (3th derivative of position)?I think it is a jerk because acceleration is changing with respect to time in SHM. Am i correct?
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### Calculating lateral/longitudinal acceleration/jerk

I know how to calculate the lateral and longitudinal velocities given the velocity $v$ and heading angle $\theta$ : $v_{lat} = v × \ \mathrm{sin} \theta$ $v_{long} = v× \cos \theta$ But does this ...
1 vote
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### Optimizing for "sudden" change in angular momentum

I'm trying to create an elaborate impossible-to-juggle juggling club, by triggering a sudden change in angular momentum via a mechanism inside of the juggling club while it is in mid-air. The ...
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### How can the jerk tend towards infinity?

Consider a block of mass $m$ kept on a rough surface. A time varying force $F =t$ is applied on the block in a direction parallel to the surface. Assuming the coefficient of static and kinetic ...
1 vote
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### High order derivatives and their impacts to a system

I'm trying to understand how high-order derivatives (Jerk, Snap, Crack, Pop and onward) impact a system and their implications to analysis. I have used Jerk in the past when considering how "...
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### Is there a limit to $\frac{d^nx}{dt^n}$? [duplicate]

There is already a question on the limit of acceleration($\frac{d^2x}{dt^2}$) and we all know the limit of velocity($\frac{dx}{dt}$) which is $c$ or the speed of light. My question is a generalized ...
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### How to determine the minimum "Arrival Distance" given a maximum velocity, acceleration and jerk along with an initial velocity and acceleration?

Problem Given the following: $A$ - maximum acceleration. $J$ - constant jerk (the rate of change of acceleration). $v$ - initial velocity. $a$ - initial acceleration (where, in practice, $a ∈ [-A, A]$...
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### How to determine the distance travelled before a maximum acceleration is reached given a constant jerk?

Problem Given: An initial velocity and acceleration of 0. A maximum acceleration $A$ A constant jerk $J$ How might one determine the distance $D$ traversed before the maximum acceleration $A$ is ...
1 vote
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### Speed, acceleration, accelerating acceleration, etc. How do we know where to stop?

I am not a physicist. Suppose a body A is falling towards body B in a vacuum. We know that A's speed will increase. However, as A draws near to B, the force of gravity will increase so the rate at ...
1 vote
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### What is the jerk parameter in terms of the Density parameters and equation of state?

In cosmology the deceleration parameter defined as the $$q_0 = \frac{1}{2}\sum_i\Omega_{i,0}(1+3w_i)$$ Is there a similar expression for the jerk parameter ($j_0$)?
1 vote
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### Why forces are functions of time, position and velocity at most? [closed]

I know that there is a quantity called jerk (USA) or jolt (UK) which is the third-order derivative of position (i.e. the first derivative of acceleration). When we write down the second law of Newton, ...
1 vote
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### Why not consider rate of change of acceleration? [duplicate]

Why do we not consider rate of change of acceleration in the study of linear motion?
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### Is there jerk on Uniform Circular Motion? [duplicate]

I was reading my textbook and I encountered a section where it explains that Centripetal Acceleration is not constant, thus, I wonder if jerk exists in Uniform Circular Motion? The textbook states ...
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### Would the jerk of this rocket be constant?

I was working on this interesting problem I came up with for a couple hours and got stuck - decided to ask here. A rocketship with is accelerating upward with constant thrust. Ignoring air resistance ...
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### What would prevent object from experiencing an infinitely powerful jerk in an instant?

Unlike speed which is capped for anything with rest mass at speed of light in a vacuum, what would prevent an object to undergo infinite acceleration in an instant? I assume in theory if we can apply ...
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### "The state-space for a single particle in classical space is 6-dimensional" -- Is this wrong?

The general argument is as follows. By Newton's second law $\mathbf F=m\ddot{\mathbf{x}}$. Now it is said that this is a second-order ODE and hence requires $\mathbf x(0)$ and $\mathbf{\dot{x}}(0)$ as ...
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### Why is jerk/jolt unintuitive as opposed to acceleration and velocity?

Going from position to velocity to acceleration makes sense. But suddenly acceleration to jerk is hard to grasp. Why is that?
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### Change in Acceleration to Elapsed Time

I am designing an algorithm. The problem statement is relatively straightforward. You are given some initial state (initial velocity and initial acceleration) as well as a target acceleration and a ...
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### Kinematic displacement: why not represent higher order rates of change?

I understand that the equation for kinematic displacement is: $x = v_{0x}t+\frac{1}{2}a_xt^2$ Perhaps my understanding is naive, but it seems like this leaves out higher order rates of change. Why ...
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### How are jerk equations connected to chaos theory?

I read in this Wikipedia article: It has been shown that a jerk equation, which is equivalent to a system of three first-order, ordinary non-linear differential equations, is the minimal setting ...
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### Imminent car crash, should I brake? [duplicate]

So I am sitting at traffic lights, stationary, in my car. A drunk driver has crossed over and is about to hit me head on at 40 mph. I only have enough time to do one thing, hit the brakes or leave ...
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### 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 ...
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### Relativity of Jerk

Popular expositions of general relativity start with a thought experiment showing that it is impossible to distinguish a constantly accelerating frame of reference in a free fall from a free floating ...
1 vote