Question

A car driving at 93m/s can stop in 75 m. What is the smallest radius the car can safely travel at the original velocity?

Answer 1

work done in stopping = brake force * 75 meters

(1/2) m v^2 = work done by brakes
(1/2) m (93)^2 = F * 75
F = m (57.66)
but F = ma
so
a = 57.66
that is the acceleration the tires can give you.
Use it for centripetal acceleration
a = 57.66 = v^2/r
r = (93)^2/57.66