the driver of a car travelling at 100km/hr suddenly sight an obstacle 50m ahead of him What maximum acceleration must be applied to the car by applying the brake in order to avoid hitting the obstacle

Answer 1

100 km/hr = 27.78 m/s
v = √(2as)
27.78 = √(100a)
a = 7.716 m/s^2

That is the minimum acceleration which will do the job. There is no maximum value.