Answer
Yes. No.
Work Step by Step
As seen in equation 6.13, the work-energy theorem, the total work on the object is the change in its kinetic energy. The total work can be negative if the change in the object’s kinetic energy is negative, i.e., if it is slowing down.
However, the magnitude of the negative total work cannot be greater than the object’s initial kinetic energy. If that were so, the final kinetic energy of the object would have to be negative. However, we know that kinetic energy is $K=\frac{1}{2}mv^2$, and kinetic energy is never negative.
