Is there any such thing as a change in acceleration (ex: 3 m/s/s/s)? If there exists something like that, then in $distance/time/time/time$, how is it expressed?
 A: 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.
A: 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 )
A: 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 $x''''''=\frac{d^6x}{dt^6}$,

*... 

A: 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.
