A block of mass moves on a horizontal surface with coefficient of friction , subject to a constant force acting vertically downward...

There are 4 forces acting on the block:gravitational force downwards,the force downwards,the reaction force upwards,the friction force horizontally.

The net force which is their vector sum, gives the block some acceleration By Newton's Second law Because the block moves horizontally, its speed and acceleration are also horizontal. Thus the net force is also horizontal that means all vertical forces are...

There are 4 forces acting on the block:
gravitational force downwards,
the force downwards,
the reaction force upwards,
the friction force horizontally.

The net force which is their vector sum, gives the block some acceleration By Newton's Second law Because the block moves horizontally, its speed and acceleration are also horizontal. Thus the net force is also horizontal that means all vertical forces are balanced, and

It is known that Therefore, the acceleration magnitude is Also it is known that friction force is opposite to the direction of movement.

Therefore, the speed of the block is and the block stops at time (when the speed becomes zero). The distance as a function of time is therefore    and the farthest distance is

This is the answer.