If the displacement is in a direction opposite to the force?

In: 0

Like you said, any time a force is being applied opposite the direction of movement. Examples would be applying a force to slow something down or when the direction of force is redirected through some means (such as a pulley system).

Not really, no. The work dome to stop an object is still work, regardless of the direction of application. It’s kinda like asking if you can have a negative speed.

Have you ever tried cleaning up after small children? That definitely feels like negative work getting done…

You can have negative work just like you have negative acceleration.

Negative work is just the removal of energy from a system, where positive work is adding energy to a system.

One example of this is block dropping with an attached spring. The string is generating an upwards force on the block, but the blocks displacement is downwards.

W = F dot s =|F|*|s|*cos(theta)

In this case, theta is pi (or -pi) radians. cos(pi) = cos(-pi) = -1. Since the magnitudes of F and s MUST be positive (magnitudes are always positive) this implies that the work done is negative.

Negative work is just having a moving object and stopping it. So yes.

If you have a block, it takes work to push that block with a force. Then, if you want to stop it, you have to make a force in the other direction. In real life this is taken care of for you by friction. So friction is a real life example of something doing negative work.