Final answer:
In this physics question, the skid marks left by a car in an accident are used to determine the car's speed. By calculating the average length of the skid marks and using the formula for speed calculation, we can find that the car was traveling at approximately 45.1 mph at the time of the accident.
Step-by-step explanation:
In this scenario, the subject relates to the physics topic of measuring skid marks to determine the speed of a vehicle. By measuring the length of the skid marks left by the car, the police can estimate the car's speed at the time of the accident.
In this case, the skid marks were measured at 47 feet, 48 feet, 52 feet, and 49 feet. To determine the car's speed, we can calculate the average length of the skid marks.
Average skid mark length = (47 + 48 + 52 + 49) / 4 = 49 feet
Now, we can use the formulas of physics to calculate the speed of the car. The skid mark length can be related to the initial speed of the car using the equation:
Final speed^2 = Initial speed^2 + 2 * acceleration * distance
Since the car came to a stop, the final speed is 0. Solving for the initial speed:
Initial speed^2 = - 2 * acceleration * distance
Using the coefficient of friction between the tires and the road as the acceleration, we can convert the distance of the skid marks from feet to meters (1 meter = 3.281 feet). Plugging in the values:
Initial speed^2 = - 2 * 0.55 * (49 * 3.281)
Simplifying the equation leads to:
Initial speed = 20.16 m/s
Converting from meters per second to miles per hour (1 m/s = 2.237 mph):
Initial speed = 20.16 m/s * 2.237 mph/m = 45.1 mph
Therefore, the average speed of the car at the time of the accident was approximately 45.1 mph. Hence, the police ticketing Brandon for speeding is justified.