# Is there any such thing as a change in acceleration (ex: 3 m/s/s/s)? [duplicate]

If there exists something like that, then in $distance/time/time/time$, how is it expressed?

• Related: physics.stackexchange.com/q/136880/2451 and links therein. – Qmechanic Apr 11 '15 at 19:29
• In fact, it is not only possible, it is necessarily the case. That is to say, uniform acceleration is not physically realizable. – Alfred Centauri Apr 11 '15 at 21:58

http://wordpress.mrreid.org/2013/12/11/jerk-jounce-snap-crackle-and-pop/

Speaking derivatives to time:

• First position $x$,
• then velocity $v=x'=\frac{dx}{dt}$,
• then acceleration $a=x''=\frac{d^2x}{dt^2}$,
• then jerk $x'''=\frac{d^3x}{dt^3}$,
• then jounce/snap $x''''=\frac{d^4x}{dt^4}$,
• then crackle $x'''''=\frac{d^5x}{dt^5}$,
• then pop $x''''''=\frac{d^6x}{dt^6}$,
• ...
• Formally, the fourth-derivitive of position is the jounce, however, someone published a paper using snap (see also the footnote on page 4). On a less serious note, when multiplied by mass, you get, respectively: kilogram-meter ($m\cdot x$), momentum ($m\cdot v$), force ($m\cdot a$), yank ($m\cdot jerk$), tug ($m\cdot snap$), snatch ($m\cdot crackle$), shake ($m\cdot pop$). – Cole Johnson Apr 11 '15 at 22:56
• In valvetrain design engineering areas of linear snap (constant pop) are used as design limits for valve lift profiles. – ja72 Apr 12 '15 at 0:02
• d4x/dt4, d5x,/dt5, d6x/dt6, Rice Crispies! – michaelsnowden Apr 12 '15 at 7:17

Yes. Rate of change of acceleration is called jerk. Yes its dimensional formula is $[M^0, L^1, T^{-3}]$. Similarly one could also define higher time derivatives of acceleration if required for a particular problem.

• There is a name for the further derivatives of acceleration too, i believe jounce is the second derivative of a, though after that its not a consensus among physicists – Triatticus Apr 11 '15 at 22:46

Yes. usually we name them $a'$ . and there can be even a speed of my $a'$ that I can call that $a''$ and it goes on like that.

it is only used it real life calculation that the calculation should be very precise like rocket science.

and the equation of displacement (with a constant $a'$) will be :

$$x =\frac16 a't^3 + \frac12 a_0t^2 + v_0t+x_0$$

(EDIT: also should mention sometimes they put a little dot on the a too instead of apostrophe )

• You might want to add that the equation holds only for constant rate of change of acceleration. – user40330 Apr 11 '15 at 19:31
• @user40330 yes good point. – Mobin Apr 11 '15 at 19:33
• Regarding the edit - yep, $\dot{b}$ indicates the change in a quantity, $b$, with respect to time: $\frac{db}{dt}$. – HDE 226868 Apr 11 '15 at 20:05
• @HDE226868 thanks. I remember one my professors mentioned that you use apostrophe (and he always used this method) to mention the second acceleration. – Mobin Apr 11 '15 at 20:08

An actual example in which there is a non-zero change in acceleration, that is, jerk, occurs is a spring. A spring's motion is described by a sinusoidal function. The derivative of a sinusoidal function is just another sinusoidal function. As a result, you can differentiate such a function infinitely many times, and will never have a derivative that's 0/a constant. So not only is there there a non-zero jerk in the motion of a spring, every single derivative of position is non-zero.