Final answer:
The driver travels a total distance of 50.83 meters before coming to a stop, missing the traffic light line by 6.83 meters. This includes the distance covered during the reaction time and the stopping distance after applying the brakes.
Step-by-step explanation:
To calculate the distance the driver misses the traffic light line, we first need to consider the distance the car travels during the driver's reaction time. The reaction time is 0.14 s, and since the car continues at a constant speed of 20.5 m/s during this time, the distance covered is:
Distance during reaction time = speed x reaction time = 20.5 m/s x 0.14 s = 2.87 m
Next, we calculate the stopping distance once the brakes are applied. The car decelerates at a rate of 4.40 m/s². Using the formula v² = u² + 2as (where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance), and rearranging it to solve for distance (s), we get:
s = (v² - u²) / (2a)
Here, the final velocity v is 0 (as the car comes to a stop), and the initial velocity u is 20.5 m/s.
So, Stopping distance = (0 - (20.5 m/s)²) / (2 x -4.40 m/s²) = 47.96 m
The total distance the car travels before stopping is the sum of the distance during the reaction time and the stopping distance:
Total distance = Distance during reaction time + Stopping distance = 2.87 m + 47.96 m = 50.83 m
This means that the driver misses the traffic light line by:
Distance missed = Total distance - Distance to the light = 50.83 m - 44.0 m = 6.83 m
Therefore, the driver misses the traffic light line by 6.83 meters.