Can the work done by a force be negative?

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Work is W = Fd cos θ, where θ is the angle between the force and the displacement. Work is a scalar, but it can be positive, zero or negative, depending on θ.

If θ < 90°, the work is positive: the force adds energy, as when you push a cart forward. If θ = 90°, the work is zero, like the normal force on a block sliding along a level floor. If 90° < θ ≤ 180°, the work is negative: the force takes kinetic energy away.

Kinetic friction on a block sliding to a stop points opposite to the block's displacement, so θ = 180° and cos θ = −1. The work done by friction is −fd. The work–energy theorem agrees: net work equals the change in kinetic energy, and the block's kinetic energy drops from ½mv² to 0, so the net work is −½mv², which is negative. (Gravity and the normal force do no work here because they are perpendicular to the horizontal displacement.)

Other examples of negative work: gravity on a ball while it rises, the brakes on a moving car, your hands when you catch a ball and slow it down. And friction is not always negative: in the ground frame, static friction on a box riding in an accelerating truck does positive work on the box. Always look at the angle.