I think the 1.5s you calculated was actually the maximum acceleration from initial velocity of 13.89ms^-1(50hm/h) to final velocity of 5.33ms^-1(20hm/h). When the question said the time for this initial velocity and final velocity was actually 2.3 seconds but what you calculated was a higher/max/unsafe acceleration. The question was actually looking for you to find the acceleration of initial velocity 13.89 to final velocity 5.33 in 2.3s which is -3.7ms^-2 is enough to stop the car before 15m assuming a complete stop so a final velocity of 0. Although you could have other interpretations of proving this. I personally mentioned the acceleration of needed to stop the car is too large to stop in 15m since it was literally double the acceleration (-6.43) to stop in time compared to the 'safe' acieration of -3.7. The amount of time required to stop at maximum acceleration is less than what the acceleration of -3.7ms^-2 would need.