Question

speed of two identical cars are u and 4u at a specific instant,the ratio of the respective distance in which the two cars are stopped from that instant by same breaking force-

Answer 1

Since the two cars are identical, they have same mass. Since the braking force is same, the retardation produced is same. 
Using the kinematics equation,
v² - u² = 2(a)(s)                                           v = final velocity, u = initial velocity,
                                                                   a = accelaration, s = displacement
For body 1 : 
            0² - u² = 2 (a) (s1)
For body 2 : 
            0² - 16u² = 2 (a) (s2)
By taking the ratio, you get s1:s2 = 1:16