Define optimum speed.

(N/A) The velocity of a vehicle on a banked circular road is given by the general formula:
$v = \left[ r g \left( \frac{\mu_{s} + \tan \theta}{1 - \mu_{s} \tan \theta} \right) \right]^{\frac{1}{2}}$
For the optimum speed,we assume the road surface is smooth,meaning the coefficient of static friction $\mu_{s} = 0$.
Substituting $\mu_{s} = 0$ into the equation:
$v_{0} = \left[ r g \left( \frac{0 + \tan \theta}{1 - 0 \cdot \tan \theta} \right) \right]^{\frac{1}{2}}$
$v_{0} = \sqrt{r g \tan \theta}$
At this speed,the horizontal component of the normal force provides the necessary centripetal force,and no frictional force is required. Driving at this speed on a banked road minimizes wear and tear on the tyres. This specific velocity $v_{0}$ is known as the optimum speed.