Consider this -
A box lies on the floor of a bus which starts accelerating. Two cases arise
$1.$ If the static friction is great enough, the box accelerates with the bus with acceleration equal to that of the bus in the direction of force
$2.$ If the static friction is not great enough, the box tries to maintain its inertia and then moves with the bus after kinetic friction kicks in.
My question is if my reasoning in the second case is not flawed, the value of kinetic friction is greater than that of static friction (this follows since there are no other forces acting on the block except friction), which is wrong.
Where is my reasoning flawed?
P.S. - In the second case, my reasoning is the static friction is in $0$, so no forces acts on the object initially, but since the floor moves away, kinetic friction increases, which causes the object to move with the bus.