  In the Special Theory of Relativity space and time intervals are different in
different frames of reference. As a consequence, the quantity 'velocity' of
classical mechanics splits into different quantities in Special Relativity,
coordinate velocity, proper velocity and rapidity. The introduction and clear
distinction of these quantities provides a basis to introduce the kinematics of
uniform and accelerated motion in an elementary and intuitive way. Furthermore,
rapidity links kinematics to dynamics and provides a rigorous way to derive
Newtons Second Law in the relativistic version. Although the covariant
tensorial notation of relativity is a powerful tool for dealing with
relativistic problems, its mathematical difficulties may obscure the physical
background of relativity for undergraduate students. Proper velocity and proper
acceleration are the spatial components of the relativistic velocity and
acceleration vectors, and thus, they provide a possibility to introduce and
justify the vectorial notation of spacetime. The use of the three different
quantities describing 'velocity' is applied to discuss the problems arising in
a thought experiment of a relativistic spaceflight.
