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.

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Show that the car will not skid if the curvature of the road is such that (with R = 1/K) (v) + R (ug) Note that braking (v' < 0) and speeding up (v'> 0) contribute equally to skidding.