As described in {numref}`ch:mechanicsintroduction`, classical mechanics is based on a set of axioms, which in turn are based on (repeated) physical observations. In order to formulate the first three axioms, we will need to first define three quantities: the (instantaneous) velocity, acceleration and momentum of a particle. If we denote the position of a particle as $\bm{x}(t)$ - indicating a vector<sup>[^1]</sup> quantity with the dimension of length that depends on time, we define its velocity as the time derivative of the position:
As described in {numref}`ch:mechanicsintroduction`, classical mechanics is based on a set of axioms, which in turn are based on (repeated) physical observations. In order to formulate the first three axioms, we will need to first define three quantities: the (instantaneous) velocity, acceleration and momentum of a particle. If we denote the position of a particle as $\bm{x}(t)$, indicating a vector<sup>[^1]</sup> quantity with the dimension of length that depends on time, we define its velocity as the time derivative of the position:
