Static or kinetic friction? Suppose i have a man standing on a plank.There exists friction between the plank and the man but there isn’t any friction between the plank and the ground. If the man starts running on the plank towards right then by conservation of momentum, the plank must have a velocity towards the left as seen from the ground.Since there is relative motion between the plank and the man,the friction acting must be kinetic. However,the answer given is that the friction maybe static or kinetic. Where am i going wrong?
 A: Unless the man exerts a backwards force that exceeds the maximum possible static friction force between his feet and the plank, he will not "slip" on the plank. That maximum static friction force is $uMg$ where $u$ is the coefficient of static friction between his feet and the plank and $M$ is the man's mass. If it is not exceeded, he will experience static friction only. If it is exceeded, he will slip on the plank and the force will be kinetic friction. So it could be static or kinetic friction, as the book says, depending on whether or not the force he exerts backwards on the plank exceeds the maximum possible static friction force.
However, since there is no friction between the plank and the ground, the only force acting on the plank is the backward force exerted by the man's feet. That net backward force will cause the plank to accelerate backwards on the ground. Per Newton's third law the backward force exerted by the man on the plank equals the forward static friction force the plank exerts on the man. If that force exerted by the man is $F$, then from Newton's second law
$$a_{plank}=\frac{F}{m}$$
$$a_{man}=\frac{F}{M}$$
where $m$ is the mass of the plank  and $a_{plank}$ and $a_{man}$ are the accelerations of the plank and man relative to the ground, all assuming the man does not slip on the plank.
Hope this helps.
A: The answer is given correct,
Static friction acts when there is "relative motion" between your shoes and the plank, and by that I mean when you run your shoes or feet are not "skidding" or "slipping" on the plank as it happens in most of the cases.
However if you run very fast or the friction is relatively low between your shoes and the plank, slipping starts, and here we can say now there is relative motion between your shoes and plank (at the point of contact), in this case kinetic friction acts.
A: This might be easier when you think of a car. Normally when a car accelerates, the bottom of the tires do not slip. Friction is static. However, if you step on the gas hard enough, you can burn rubber. The tires slip. In that case, friction is kinetic.
It is a bit of a stretch for a running man to accelerate hard enough to burn rubber on the bottom of his shoes if he is on a street. But he might step on a banana peel or patch of ice, or just run on a dirt road.
Now add in the plank. It is possible for a foot to slip on a plank or a plank to slip on a road. There are two coefficients of friction. It isn't clear which is larger. It depends on the kind of shoes, plank, and road. You can imagine a plank on an icy road, or a shoe with some oil on it.
A: As the earlier answer explained I will try to give an another example.
Suppose the man moon walk's and reach the other end . Since the point of contact between his feet and plank was relatively moving friction is kinetic here.
Now in another case the man tip toe and reach the other . To imagine that try placing your two fingers on desk and move it . You will observe that point of contact that is the point on the finger that touches the ground is at rest (reletive to ground) . In this friction is static.
