The work-kinetic energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In the case of a particle sliding on a surface, the force of sliding friction acts in the opposite direction to the motion of the particle, and therefore does negative work on the particle. This negative work reduces the kinetic energy of the particle, causing it to slow down.

Mathematically, the work-kinetic energy theorem can be expressed as:

$$W_{net}=\Delta K$$

where:

- $$W_{net}$$ is the net work done on the object

- $$\Delta K$$ is the change in kinetic energy of the object

In the case of a particle sliding on a surface, the net work done on the particle is equal to the work done by the force of sliding friction:

$$W_{net}=F_fd$$

where:

- $$F_f$$ is the force of sliding friction

- $$d$$ is the distance over which the particle slides

The change in kinetic energy of the particle is equal to the negative of the work done by the force of sliding friction:

$$\Delta K=-W_{net}=-F_fd$$

Since the force of sliding friction is always positive, the change in kinetic energy is always negative, which means that the kinetic energy of the particle decreases as it slides on the surface. This decrease in kinetic energy is what causes the particle to slow down.

The work-kinetic energy theorem provides a quantitative explanation for why the force of sliding friction reduces the kinetic energy of a particle.