The frictional force between the feet of a man and the ground is static in nature.
These lines are taken from a reputed book. I was confused with this. Firstly, the feet is moving relative to the ground. So, why can't the friction be kinetic in nature. Secondly, for the frictional force to be static $f_s = ma$ , so while walking with constant velocity we get $f = 0$ but this cannot be true because we know that friction is necessary for walking.
Update I deduced that: The contact force exerted by the man on the ground and that exerted by the ground are action reaction pairs. When the vertical component of the contact force exerted on the man by the ground, exceeds the weight of the man, the contact is broken between man and ground and the contact force does not act. So, it can be concluded that the horizontal component of this reaction force acts for this time interval $dt$ when the foot is not moving relative to the ground. Hence the friction is static in nature.
But this raises some obvious questions : If friction acts only for this small time interval $dt$ at the point of contact(the feet of the man), can it affect the motion of the centre of mass of the man? Considering the part of the time the foot is in the air, does friction has anything to do with affecting the motion of the man? A force is always essential for motion. Since the only horizontal component acting on the man is friction, what exactly happens different while walking with constant velocity and while accelerating?