A woman pushes a 35.0 kg object at a constant speed for 10.8 m along a level floor, doing 280 J of work by applying a constant horizontal force of magnitude F on the object. (a) Determine the value of F (in N). (Enter the magnitude.) N (b) If the worker now applies a force greater than F, describe the subsequent motion of the object. The object's speed would increase with time. The object's speed would remain constant over time. The object would slow and come to rest. (c) Describe what would happen to the object if the applied force is less than F. The object's speed would increase with time. The object's speed would remain constant over time. The object would slow and come to rest.

By definition of work, this is the process through which a force applied on an object, produces a displacement of the object.
If the force is constant, and the displacement is parallel to the direction of the force, this work is just the product of the applied force times the distance, as follows:

[tex]W = F_{app} * d (1)[/tex]

[tex]F_{app} =\frac{W}{d} = \frac{280J}{10.8m} = 25.9 N (2)[/tex]

b)

If the object is moving at constant speed when it is applied a force F, this means that this force must be compensated by an equal opposite force, in this case, the kinetic friction force.
Since this force is constant while the object is moving, if we increase the force F making it larger, there will be a net force in the direction of the displacement, which will cause an acceleration that will increase the speed with time.

c)

We have already said in b) that if the object is moving at constant speed, there must be an equal and opposite force to the applied force F, the kinetic friction force, which is constant, acting on the object.
If we apply a force less than F, there will be a net force in the direction opposite to the displacement, that will cause a acceleration opposite to the displacement, which will make the object to slow down and eventually come to rest.