When a body is moving on a surface,the force of friction is called

With what minimum velocity should a block be projected from the left end $A$ towards end $B$ such that it reaches the other end $B$ of a conveyor belt moving with a constant velocity $v$ towards the left? The length of the belt is $L$ and the coefficient of friction between the block and the belt is $\mu$.

$A$ uniform rod of length $L$ and mass $M$ is placed on a rough horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod such that the rod is just in the state of rest. The coefficient of friction varies according to the relation $\mu = Kx$,where $K$ is a positive constant and $x$ is the distance from the end where the force is not applied. Find the tension at the midpoint of the rod.

$A$ small block of mass $m$ is projected horizontally with speed $u$. The coefficient of friction between the block and the plane is given by $\mu = cx$,where $x$ is the displacement of the block on the plane. Find the maximum distance covered by the block.

$A$ block is thrown with a velocity of $2 \, m/s$ (relative to the ground) on a belt,which is moving with a velocity of $4 \, m/s$ in the opposite direction of the initial velocity of the block. If the block stops slipping on the belt after $4 \, s$ of throwing,then choose the correct statement$(s)$:

$A$ horizontal force of $129.4 \, N$ is applied on a $10 \, kg$ block which rests on a horizontal surface. If the coefficient of friction is $0.3$,the acceleration should be ....... $m/s^2$.