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.