A car is taking an unbanked curve. if you have the information about the radius of the curve and the coefficient of the static friction between tires and concrete, how can you determine the maximum speed with which the car can negotiate the curve without sliding out

The normal force on a level roadway is that due to acceleration by gravity of the mass of the car. The magnitude of the radial force that can be supported without slipping is the product of the normal force and the coefficient of static friction. The magnitude of the radial force required to turn the car is the ratio of the product of the car's mass and the square of its speed to the radius of the curve. That is

kmg = mv²/r

The mass of the car cancels when we solve for v, the maximum speed in the curve:

v = √ (kgr)

where k is the friction coefficient, g is the acceleration due to gravity, and r is the radius of the curve.