Final answer:
By calculating the total stopping distance accounting for the driver's reaction time and the braking deceleration, we find that the car, approaching a traffic light at 54 km/h with a 0.4-second delay before braking and decelerating at 3.75 m/s², would require 36 m to come to a stop. However, as the traffic light is only 30 m away, the car will not stop in time.
Step-by-step explanation:
To determine whether the car can stop in time when it approaches a traffic light at 54 km/h, considering a delay of 0.4 seconds before applying the brakes and a slow-down rate of 3.75 m/s², we need to calculate the total stopping distance and compare it with the distance to the traffic light. First, we convert the car's speed from km/h to m/s: 54 km/h = 15 m/s. During the reaction time of 0.4 seconds, the car travels a distance without slowing down, which is found by multiplying the speed by the reaction time. This distance is reaction = speed × reaction time = 15 m/s × 0.4 s = 6 m.
Next, we calculate the distance needed to stop after applying the brakes, which can be found using the formula braking = v² / (2×a), where v is the initial speed and a is the deceleration. Thus, dbraking = (15 m/s)² / (2× 3.75 m/s²) = 30 m. Therefore, the total stopping distance is the sum of the distance traveled during the reaction time and the braking distance: total = reaction + braking = 6 m + 30 m = 36 m. The distance to the traffic light is 30 m, but the car requires 36 m to stop. Therefore, the car will not be able to stop in time and will run the red light.