Final answer:
Vehicle tires should be replaced when the tread depth is less than 1.5 mm to ensure safety. The physics problems involve finding the number of tire revolutions over a certain distance and calculating frequency of tread vibrations given a certain speed. Pressure changes in tires due to temperature changes can be calculated using the ideal gas law.
Step-by-step explanation:
The question concerns the replacement of a vehicle's tires when the tread depth reaches a certain limit. According to most safety standards, this depth is considered to be 1.6 mm (which is not listed as an option in this question), but for the sake of addressing the given choices, 1.5 mm (option a) is the closest and would be considered unacceptable for safe driving.
Now, related to the questions about tire wear and characteristics:
Question about revolutions of a tire (3)
An automobile with 0.260 m radius tires travels 80,000 km before the tires wear out. To find out how many revolutions the tires make, consider the circumference of a tire (2 x π x radius) and then divide the total distance traveled by the circumference.
Question about tread vibration frequency (11)
A tire has a tread pattern with a crevice every 2.00 cm. Given that the car moves at 30.0 m/s, you can find the frequency of vibrations by taking the speed of the car and dividing it by the distance between crevices (converted to meters), since frequency is the inverse of the time it takes to move from one crevice to the next.
Question about pressure change in tires (22)
The gauge pressure in car tires changes with temperature changes according to the ideal gas law. When the temperature drops, the pressure also drops. The specific calculation would involve using the initial and final temperatures and pressures and applying the ideal gas law, considering the volume is constant.