position , velocity , acceleration , jerk

glossary

• differentiation

A one-dimensional position can be expressed as a number.
Since time exists, let $d(t)$ be a function that returns the number for a given time, $t$.

Velocity is the rate of change of an object’s position over time
$v(t)=d^{\prime }(t)$

Acceleration is the rate of change of an object’s velocity over time
$a(t)=v^{\prime }(t)=d^{\prime \prime }(t)$

Jerk is the rate of change of an object’s acceleration over time
$j(t)=a^{\prime }(t)=v^{\prime \prime }(t)=d^{\prime \prime \prime }(t)$