As a comet approaches the Sun, it arcs around the Sun more rapidly. Why?

According to Kepler's law a radius vector joining planet and sun swept equal area in equal interval of time thus it can be applied for comets.

when a comet is nearer to sun it has to swept more area so its velocity is more nearer to the sun,

The basics of this formula comes from conservation of angular momentum thus comet moves faster when it approaches the sun.