Analyzing an Auto Accident: Calculating Car A's Speed Before Collision

What was the speed of car A just before the collision? Car A, with a mass of 1400 kg, collides with Car B, which was stopped at a red light. The cars lock bumpers and slide to a stop. Measurements show the skid marks left by the tires are 7.20 m long, with a coefficient of kinetic friction of 0.65. By analyzing the collision and applying principles of physics, we can calculate the speed of Car A just before the collision.

To determine the speed of car A just before the collision, we need to consider the principles of collision, conservation of momentum, and kinetic energy. The work-energy theorem and the concept of conservation of momentum will help us in this analysis.

Calculating Car A's Speed:

First, we calculate the work done by the friction force, which is equal to the kinetic energy present in the system. This can be determined using the formula:

Uc₂f = √(2μkgd)

Where:
- μk is the coefficient of kinetic friction (0.65 in this case)
- k is the gravitational acceleration
- d is the distance of the skid marks (7.20 m)

By substituting the given values into the formula, we can solve for the initial speed of Car A just before the collision. The resulting speed will be in meters per second (m/s).

Once we have calculated the initial speed of Car A in m/s, we can convert this value to miles per hour (mph) to understand how fast Car A was traveling. By comparing this speed to the legal speed limit of 35 mph, we can determine by how many mph Car A was exceeding the speed limit.

By utilizing the principles of physics and the data provided, we can accurately calculate the speed of Car A and gain insights into the dynamics of the auto accident. Understanding the physics behind collisions and momentum conservation allows us to analyze and interpret the events leading up to the collision with precision.

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