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Which statement about work is true?

The work done is negative when the force is in the opposite direction to displacement

The work done is positive when the force and displacement align

Work is zero when there is no displacement

All of the above

The key idea is that work depends on how the force compares to the motion it causes, and it’s quantified by the dot product W = F · d. This means the sign and amount of work come from how much of the force acts in the direction of the displacement.

If the force points opposite to the direction of motion, the component of force along the displacement is negative, so the work done is negative. If the force points in the same direction as the motion, the force has a positive component along the displacement, giving positive work. If there is no displacement at all, there’s no distance over which the force can act, so the work is zero regardless of the force.

Putting these together shows all the statements are true: negative work can occur when the force and displacement oppose each other, positive work occurs when they align, and zero work happens when there is no displacement.