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Answer :
Final answer:
This problem involves using principles from physics, specifically kinematics and dynamics, to calculate the initial velocity of a vehicle involved in an accident, based on the length of the skid marks it left on the road. The solution applies the work-energy theorem and accounts for factors such as the condition of the road and the final state of the vehicle (brought to a full stop).
Explanation:
The question involves calculating the initial velocity of a vehicle after an accident based on the length of the skid marks left on the avenue. Given that the vehicle struck a fire hydrant and the road conditions were wet, it invokes principles of physics specifically in the domain of kinematics and dynamics.
Here's how we're going to calculate the initial velocity of the vehicle: using the work-energy theorem. This theorem states that the work done on an object is equal to the change in its kinetic energy. In the case of a car skidding to a stop, the work done (resistance force by the road times distance) results in a reduction of kinetic energy to zero since the car is eventually brought to a full stop.
Final velocity2 = Initial velocity2 + 2 × acceleration × distance
Knowing the length of the skid marks (120 feet), assuming an approximate coefficient of kinetic friction for wet concrete (μ ≈ 0.6), and the fact that the car was brought to a halt (final velocity = 0), we can solve the formula 1/2mv²_initial = f_kd for the initial velocity, where f_k = μmg is the kinetic friction force and d is the skid distance.
We can compute the initial velocity in meters per second and then convert this to miles per hour. It may result in a velocity that can provide insights on if the car was potentially above the speed limit at the time of the accident, which is useful information for an accident investigation.
Learn more about Physics of Vehicle Accidents here:
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