Editing Function of a real variable (section)

===Relation to kinematics===

[[File:Kinematics.svg|thumb|300px|Kinematic quantities of a classical particle: mass ''m'', position '''r''', velocity '''v''', acceleration '''a'''.]]

The physical and geometric interpretation of ''d'''''r'''(''t'')/''dt'' is the "[[velocity]]" of a point-like [[particle]] moving along the path '''r'''(''t''), treating '''r''' as the spatial [[position vector]] coordinates parametrized by time ''t'', and is a vector tangent to the space curve for all ''t'' in the instantaneous direction of motion. At ''t'' = ''c'', the space curve has a tangent vector {{nowrap|''d'''''r'''(''t'')/''dt''{{!}}<sub>''t'' {{=}} ''c''</sub>}}, and the hyperplane normal to the space curve at ''t'' = ''c'' is also normal to the tangent at ''t'' = ''c''. Any vector in this plane ('''p''' − '''a''') must be normal to {{nowrap|''d'''''r'''(''t'')/''dt''{{!}}<sub>''t'' {{=}} ''c''</sub>}}.

Similarly, ''d''<sup>2</sup>'''r'''(''t'')/''dt''<sup>2</sup> is the "[[acceleration]]" of the particle, and is a vector normal to the curve directed along the [[Radius of curvature (mathematics)|radius of curvature]].