If walking is a result of the reaction to a kick backwards to the ground (reaction being friction), it appears that it should be true that the kick will have to be less than the kinetic friction (which is less than the static friction threshold = $\mu$mg) or the acceleration will never be more than $\mu$g. What happens if the kick exceeds this force, there still has to be a reaction? Is that reaction distinguished from the kinetic friction?
[Physics] Walking and friction
frictionnewtonian-mechanics
Related Solutions
The problem with this question is that static friction and kinetic friction are not fundamental forces in any way-- they're purely phenomenological names used to explain observed behavior. "Static friction" is a term we use to describe the observed fact that it usually takes more force to set an object into motion than it takes to keep it moving once you've got it started.
So, with that in mind, ask yourself how you could measure the relative sizes of static and kinetic friction. If the coefficient of static friction is greater than the coefficient of kinetic friction, this is an easy thing to do: once you overcome the static friction, the frictional force drops. So, you pull on an object with a force sensor, and measure the maximum force required before it gets moving, then once it's in motion, the frictional force decreases, and you measure how much force you need to apply to maintain a constant velocity.
What would it mean to have kinetic friction be greater than static friction? Well, it would mean that the force required to keep an object in motion would be greater than the force required to start it in motion. Which would require the force to go up at the instant the object started moving. But that doesn't make any sense, experimentally-- what you would see in that case is just that the force would increase up to the level required to keep the object in motion, as if the coefficients of static and kinetic friction were exactly equal.
So, common sense tells us that the coefficient of static friction can never be less than the coefficient of kinetic friction. Having greater kinetic than static friction just doesn't make any sense in terms of the phenomena being described.
(As an aside, the static/kinetic coefficient model is actually pretty lousy. It works as a way to set up problems forcing students to deal with the vector nature of forces, and allows some simple qualitative explanations of observed phenomena, but if you have ever tried to devise a lab doing quantitative measurements of friction, it's a mess.)
Best Answer
Depending on if you kick into the ground or place your foot firmly on the ground and then "kick" to move forward, you either have to kick with less force than the threshold values for kinetic or static friction respectively to maintain "normal" walking.
Overcoming this threshold value will result in your foot having a relative velocity to the ground, or in laymans terms, you will slip and slide. This does not mean you can not maintain walking, you will just not be able get a firm foothold. When sliding like this, the friction you experience is the kinetic friction threshold value, meaning you will not be able to use more force to accelerate your body than this value. This for example happens when you thrust too hard while walking on ice.