Final answer:
At 30 mph, with an estimated reaction time of 0.5 seconds, a vehicle will cover about 6.7 meters during the driver's reaction time before the brakes are applied.
Step-by-step explanation:
When driving at 30 mph (approximately 13.4 m/s), reaction time is the interval between the moment a driver perceives a hazard and the moment they actually start to take corrective action, such as applying the brakes. Reaction times can vary, but for calculation purposes, they're often estimated to be around 0.5 to 1.5 seconds, depending on various factors including the driver's attentiveness and physical condition. The question appears to be related to calculating stopping distances and reaction times, often a crucial part of a high school physics curriculum.
In the scenario provided, the driver has a reaction time of 0.5 seconds. When traveling at 30 mph, or equivalent to 13.4 m/s, the car will cover additional distance during the driver's reaction time before the brakes are even applied. Using the formula x = vt, where x is the distance traveled, v is the velocity (13.4 m/s), and t is the time (0.5 s), we can calculate that the car would travel approximately 6.7 meters during the driver's reaction time. This distance needs to be added to the overall stopping distance when considering the total distance required to avoid a collision.