The work-energy theorem states that the net work done on the car equals its change in kinetic energy, $W_{net} = \Delta K$. The only horizontal force is friction, so $W_{net}$ is the work done by friction, $W_f$.

The work done by friction is $W_f = -f_k d$, where $f_k$ is the kinetic friction force and $d$ is the stopping distance. On a horizontal surface, the normal force $N = mg$, so $f_k = \mu N = \mu mg$.

$$W_f = -\mu mgd$$

The change in kinetic energy is:

$$\Delta K = K_f - K_i = 0 - \frac{1}{2}mv^2$$

Equating work and change in kinetic energy:

$$-\mu mgd = -\frac{1}{2}mv^2$$

Solving for the distance $d$:

$$d = \frac{mv^2}{2\mu mg} = \frac{v^2}{2\mu g}$$