What force must the worker exert to get the box moving & what force must the worker exert to accelerate the box at 0.1 meters per second squared to the south?

Since static friction is the minimum force required to just start the motion of a stationary object.

Here if we need to start an object from rest then we required F = 700 N

So for the first part of the above problem Force will be F = 700 N

Now if the box is already moving then we will have to use kinetic friction force between box and floor

now we can write the equation of net force as

here

now we will have