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 umg, where µ is the co- efficient of friction and g = 9.8 m/s². Let v be the car's speed in meters per second. Show that the car will not skid if the curvature k 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.

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 umg, where µ is the co- efficient of friction and g = 9.8 m/s². Let v be the car's speed in meters per second. Show that the car will not skid if the curvature k 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.