Work can be either positive or negative, but some care is needed to get the sign right when calculating work. The key is to remember that work is an energy transfer. If the force causes the particle to speed up, then the work done by that force is positive. Similarly, negative work means that the force is causing the object to slow and lose energy.

The sign of W is not determined by the direction the force vector points. That’s only half the issue. The displacement $\text{Δ}s$ also has a sign, so you have to consider both the force direction and the displacement direction. As FIGURE 9.4 shows, work is positive when the force acts in the direction of the displacement (causing the particle to speed up). Similarly, work is negative when force and displacement are in opposite directions (causing the particle to slow). And there’s no work at all $(W=0)$ if the particle doesn’t move!

FIGURE 9.4 How to determine the sign of W.