Part a
Answer: NO
We need to calculate the distance traveled once the brakes are applied. Then we would compare the distance traveled and distance of the barrier.
Using the second equation of motion:

where s is the distance traveled, u is the initial velocity, t is the time taken and a is the acceleration.
It is given that, u=86.0 km/h=23.9 m/s, t=0.75 s, 

Since there is sufficient distance between position where car would stop and the barrier, the car would not hit it.
Part b
Answer: 29.6 m/s
The maximum distance that car can travel is 
The acceleration is same, 
The final velocity, v=0
Using the third equation of motion, we can find the maximum initial velocity for car to not hit the barrier:

Hence, the maximum speed at which car can travel and not hit the barrier is 29.6 m/s.
Displacement (between time 0 and time 25) is the area under the velocity time curve, i.e. ∫ vdt.
Here, v(0)=10, v(25)=34 (approx.)
Therefore
displacement = (1/2)(10+34 m/s)*(25-0) s [ trapezoid area ]
=550 m