Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 5 m/s2 for 4.2 seconds. It then continues at a constant speed for 11.1 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 321.74 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop. How far does the blue car travel before its brakes are applied to slow down?
To find the distance traveled by the blue car before applying the brakes, we need to calculate the distance traveled during the acceleration and constant speed phases separately.
1. Distance during acceleration:
The blue car accelerates uniformly at a rate of 5 m/s^2 for 4.2 seconds. To find the distance traveled during this time, we can use the equation:
distance = 0.5 * acceleration * time^2
Substituting the given values:
distance = 0.5 * 5 m/s^2 * (4.2 s)^2
distance = 0.5 * 5 m/s^2 * 17.64 s^2
distance = 44.1 m
So, the blue car travels 44.1 meters during the acceleration phase.
2. Distance during constant speed:
The blue car then continues at a constant speed for 11.1 seconds. Since speed is constant, distance traveled can be calculated using:
distance = speed * time
Given that the speed is constant and not provided, we can calculate it using the information that the blue car travels a total distance of 321.74 meters before coming to rest.
distance = 321.74 m - 44.1 m (distance covered during acceleration phase)
distance = 277.64 m
So, the blue car travels 277.64 meters at a constant speed.
Therefore, the blue car travels a total distance of 44.1 meters during acceleration and 277.64 meters at constant speed, before applying the brakes to slow down.