  Friction is a complicated phenomenon involving nonlinear dynamics at
different length and time scales[1, 2]. The microscopic origin of friction is
poorly understood, due in part to a lack of methods for measuring the force on
a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4]
Despite enormous advance in experimental techniques[5], this combination of
small length scale and high velocity remained illusive. Here we present a
technique for rapidly measuring the frictional forces on a single asperity (an
AFM tip) over a velocity range from zero to several cm/s. At each image pixel
we obtain the velocity dependence of both conservative and dissipative forces,
revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We
explain measurements on graphite using a modified Prandtl-Tomlinson model that
takes into account the damped elastic deformation of the asperity. With its
greatly improved force sensitivity and very small sliding amplitude, our method
enables rapid and detailed surface mapping of the full velocity-dependence of
frictional forces with less than 10~nm spatial resolution.
