The car was traveling at approximately 80 ft/s when the brakes were first applied.
To determine the car's initial speed when the brakes were applied, the equation of motion vf^2 = vi^2 - 2as is employed, where:
vf is the final velocity (0 ft/s, as the car came to a stop),
vi is the initial velocity (the sought-after value),
a is the acceleration (-16 ft/s^2, reflecting deceleration), and
s is the skid marks distance (200 ft).
Substituting the given values into the equation yields:
0 = vi^2 - 2(-16)(200)
Simplifying, we get:
vi^2 = 6400
Taking the square root of both sides, we find:
vi = √6400
Calculating this yields:
vi ≈ 80 ft/s
Hence, the car was traveling at approximately 80 ft/s when the brakes were first engaged.
This deduction relies on the assumption that deceleration is constant and that no external forces act on the car during the braking process.
Skid marks are often used to estimate the braking distance, providing crucial information for accident reconstruction and understanding the events leading to a stop.
In this scenario, the calculated initial speed aids in evaluating the severity of the braking maneuver and contributes to an analysis of the driving conditions or any potential issues with the braking system.