Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Acceleration of acceleration

  1. Oct 9, 2005 #1
    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
    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. jcsd
  3. Oct 9, 2005 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

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

  4. Oct 9, 2005 #3
    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.
  5. Oct 9, 2005 #4


    User Avatar
    Science Advisor
    Gold Member

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

    [tex]\vec{j} = \frac{d\vec{a}}{dt} = \frac{d^3\vec{x}}{dt^3}[/tex]

    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:
    [tex]\frac{d\vec{j}}{dt} = \frac{d^4\vec{x}}{dt^4}[/tex]
    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.
  6. Oct 9, 2005 #5
    Thank you very much...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook