Friction is only independent of area of contact between two
metals because the two surfaces are not flat and only touch at a few points where tiny
projections on the two surfaces meet (and cold weld). With a tyre the radial tyres are
generally thought to be better because they are stronger because of the way in which they
are constructed. The tread on tyres removes water from the tyre in the wet to prevent the
tyre "planing" on the water.
As regards kinetic friction.
The equations usually
assume a constant of kinetic friction that is independent of the velocity – and not as you
suggest.
With cars braking to a stop the frictional forces in the brakes are assumed
to be the same whatever the speed of the car. This enables stopping distances to be worked
out. However it is a bit more complicated than that. If we assume that the car does not skid
there is no relative motion between the tyres and the road and so we can use the static
friction coefficient here.
However the frictional drag of an object falling through a
fluid does depend on the velocity of the object. The drag increases up to a point where the
drag is equal to the weight of the object and the object then falls at its terminal velocity. The
drag force is usually taken as proportional to velocity squared.
At low speeds the
kinetic friction is a stick-slip motion as the "welds" between the surfaces are constantly
broken and then reform. At higher speeds there is not time for the welds to reform and this
might suggest the lowering of the friction at higher relative speeds.