Thank you for visiting A vehicle is test skidded on a level asphalt surface asphalt tex f 0 70 tex and then on an adjacent gravel shoulder gravel tex. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The initial speed of a vehicle can be estimated by capturing the energy lost due to friction with road surfaces during a skid. This involves calculating the lost kinetic energy over both surfaces (asphalt and gravel), and solving for the initial speed through the kinetic energy formula.
Explanation:
The subject of this question is physics, specifically the physics of motion and friction. The speed of the vehicle at the beginning of the skid can be calculated using the physics formula to determine speed based on distance and friction.
First, let's calculate the kinetic energy lost when the vehicle skidded on both surfaces, using the formula KE = f * m * g * d, where: f = friction coefficient, m = mass (unknown but it'll cancel out), g = gravity constant (9.8 m/s², roughly equivalent to 32.2 ft/s²), and d = distance.
The sum of the kinetic energy lost on both surfaces (asphalt and gravel) equals the initial kinetic energy of the vehicle (1/2) * m * v². Since we're not given the mass (m) of the vehicle, we can omit this term because it cancels out on both sides of the equation. The frictional force coefficients (f) are given as asphalt f = 0.70, and gravel f = 0.45. Skid distance on asphalt is 130 feet and on gravel is 30 feet.
By applying the kinetic energy formula, the total kinetic energy over both surfaces becomes: KEasphalt + KEgravel = 0.70 * 32.2 * 130 + 0.45 * 32.2 * 30
This sum equals the initial kinetic energy: (1/2) * v²
Solving for v (the initial speed or velocity), we obtain the square root of (2 * total KE). This will give you the speed of the vehicle in feet per second. To convert it to miles per hour (if needed), multiply the result by 0.682.
Learn more about Determining Speed through Energy Conversion here:
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