Adriver has a reaction time of 0.50 s , and the maximum deceleration of her car is 6.0 m/s2 . she is driving at 20 m/s when suddenly she sees an obstacle in the road 50 m in front of her.

I will assume that you want to know if the driver can stop before hitting the obstacle or not.

First step is to use the reaction time in order to know how far can she go before her motion starts to slow:
distance = velocity x time = 20 x 0.5 = 10 m
Thus, the driver has 50 - 10 = 40 m to stop before colliding

Second step is to calculate the distance that the driver requires to stop using the rules of velocity and distance:
1- velocity = acceleration x time 
     20 = 6t > thus, time = 3.334 seconds
2- distance = 0.5 x a x t^2 = 0.5 x 6 x (3.334)^2 = 33.3466 m

From the previous calculations, we can see that the driver has 40 m to stop and she needs only 33.3466 m to stop based on the given parameters. This means that she can stop before collision.