Final answer:
Tire condition greatly affects stopping distance, which depends on factors like the coefficient of friction and tire quality. Physics equations considering friction and stopping distance can determine if the speed exceeded the limit, potentially justifying contesting a speeding ticket.
Step-by-step explanation:
The condition of a vehicle's tires significantly affects its stopping distance, which is the distance a car travels from the time the brakes are applied until it comes to a complete stop. The effectiveness of the brakes, the tire quality, and the coefficient of friction between the tires and the road surface all play crucial roles in determining the stopping distance. When the student mentioned leaving a skid mark of 30.5 meters after slamming on the brakes, this indicates a high initial speed, especially with a high friction coefficient of 0.55.
If we apply the physics of motion and the relationship between friction, deceleration, and stopping distance, we can analyze whether the skid mark length corresponds to a speed exceeding the limit. Since the stopping distance increases exponentially with speed, a car traveling twice as fast doesn't simply stop in twice the distance—it travels much further before it can stop.
Considering reaction time, brake effectiveness, and road conditions, and assuming a known friction coefficient, we use physics equations to estimate the speed of the vehicle at the time the brakes were applied. If the calculations suggest the car was indeed traveling over the speed limit, then the ticket was justified. However, if the calculations indicate a speed within the limit, fighting the speeding ticket in court could be an option with the aid of friction between the tires and the road as a central argument.