# Acceleration of acceleration

1. Oct 9, 2005

### Trepidation

Acceleration is motion at a velocity that is in a consistent state of change, right? So...

v is in terms of m/s
a is in terms of m/s^2

So what is motion at an acceleration that is in a consistent change?

a^2 is in terms of m/s^3
or
a^2 is in terms of m/s^4
?

Is this 'acceleration of acceleration' ever used? Howabout acceleration of acceleration of acceleration, etc etc ad infinitum?

2. Oct 9, 2005

### ZapperZ

Staff Emeritus
Just because something has a mathematical expression doesn't mean it is automatically physically useful or meaningful.

Zz.

3. Oct 9, 2005

### Trepidation

I know... The first part of my question was what the mathematical expression would be, and the second part was whether it would or would not be physically useful.

4. Oct 9, 2005

### jcsd

I don't think it's a^2 you want.

$$\vec{j} = \frac{d\vec{a}}{dt} = \frac{d^3\vec{x}}{dt^3}$$

j is called 'jerk' (or sometimes 'jolt') and has units of m/s^3.

In physics jerk is rarely used, though in some areas of engineering (rollercoaster design would be the usual example) it is important.

The quantity:
$$\frac{d\vec{j}}{dt} = \frac{d^4\vec{x}}{dt^4}$$
is often called 'jounce' and has even more limited use than jerk. Obviously you can keep on taking higher derivaives of dispalcement with respect to time without limit, but generally the higher the derivative the less it's use.

5. Oct 9, 2005

### Trepidation

Thank you very much...