Final answer:
Yes, you will hit the other car because during your reaction time of 0.75 seconds, you travel 23.25 meters, which is more than the 22.5 meters that separated the two vehicles. You can't even begin to decelerate before colliding with the stopped car.
Step-by-step explanation:
When you are traveling in your car at 31 m/s and are 22.5 m behind another car also traveling at 31 m/s, and the car in front of you suddenly stops, we need to determine whether or not you can stop in time. Considering your reaction time is 0.75 s, during which you continue to travel at 31 m/s, you will cover a distance equal to the speed multiplied by the reaction time:
Distance = Speed × Reaction Time
In this case:
Distance = 31 m/s × 0.75 s = 23.25 m
So, after reacting, you've actually already moved beyond the other car, which indicates you will hit the car. This calculation shows that even without applying the brakes, you've closed the 22.5 m gap during your reaction time alone. Since the maximum acceleration for each car is given as 10 m/s², this is irrelevant because the impact has already occurred before you could even begin to decelerate.In conclusion, based on the distance covered during your reaction time alone, you will hit the other car before being able to apply the brakes.