newtonian mechanics - Man inside an accelerating train carriage

I'm having trouble recognizing the forces at play here.

If we have a man is standing inside a train carriage which is accelerating, and the coefficient of friction (for simplicity dynamic and static friction constants are the same) between the man and the floor of carriage isn't enough for him to stand stationary, how do we find out his resulting acceleration?

What is the force causing the resulting acceleration to be in the opposite direction? If it's the friction between the man and the moving train, isn't it the same for the opposite direction as well? What am I missing?

Answer

Ignore non-inertial frames of reference and pseudo forces - they will only confuse you.

If the man has weight $mg$ then the frictional force exerted on the man by the floor of the train is $\mu mg$, and so that man's acceleration is $\frac{\mu mg}{m}=\mu g$.

Note that this is true relative to any inertial frame of reference - acceleration is not affected by adding or subtracting a constant velocity.

The train's acceleration $a_{train}$ must be greater than $\mu g$, otherwise a frictional force less than $\mu mg$ would be sufficient to accelerate the man at the same rate as the train. So relative to the train the man is accelerating backwards at a rate $a_{train}-\mu g$.