I know this may seem a weird question, but it always bothers me. My physics book (Resnick,Halliday,Walker), and also various sites never say anything beyond acceleration.
But when a moving body is being acted by a variable force , its acceleration will definitely change: it will either increase or decrease. Then there will be rate of change of acceleration with respect to time. So, why don't books mention this? What is the cause for not measuring $\frac{d\vec{a}}{dt}$ ? If it exists, what is the use of it?
Answer
Your question is not weird; it is legitimate. It is possible, it exists, can be of use and it is called jerk, jolt, surge or lurch, and is defined by any of the following equivalent expressions: $$\vec j(t)=\frac {\mathrm{d} \vec a(t)} {\mathrm{d}t}=\dot {\vec a}(t)=\frac {\mathrm{d}^2 \vec v(t)} {\mathrm{d}t^2}=\ddot{\vec v}(t)=\frac {\mathrm{d}^3 \vec r(t)} {\mathrm{d}t^3}=\overset{...}{\vec r}(t)$$
It is useful in the Dirac-Lorenz equation (as Emilio linked).
In case you are asking yourself, a fourth derivative (rate of jerk) is also defined, and it is called jounce
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