We consider an automobile of mass m traveling along a curved but level road. To avoid skidding, the road must supply a frictional force F = ma, where a is the car’s acceleration vector. The maximum magnitude of the frictional force is μmg, where μ is the coefficient of friction and g = 9.8 m/s². Let v be the car’s speed in meters per second.

Suppose that the maximum radius of curvature along a curved highway is R = 180 m. How fast can an automobile travel (at constant speed) along the highway without skidding if the coefficient of friction is μ = 0.5