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Finding the Speed of a Car from 190-Foot Skid Marks
Problem: After a car accident, the skid marks for one car measured 190 feet. Using the formula , find the speed of the car before the brakes were applied, rounding to the nearest tenth.
- Read the problem.
- Identify: The speed of the car.
- Name: Let = the speed in miles per hour.
- Translate: Write the skid marks formula and substitute :
- Solve: Multiply inside the radical: . Evaluate the square root:
Round to one decimal place: .
- Check: Substitute back: , so The approximation is consistent. Is 67.5 mph a reasonable speed for a car? Yes. ✓
- Answer: The speed of the car was approximately 67.5 miles per hour.
Because is not a perfect square, a calculator is needed to approximate the square root. The answer is then rounded to the specified decimal place. This example demonstrates that real-world applications of square root formulas often produce irrational results requiring approximation.
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Elementary Algebra @ OpenStax
Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax
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Finding the Speed of a Car from 190-Foot Skid Marks
Accident investigators use a specific square root formula to estimate a vehicle's speed based on the length of skid marks. Which of the following correctly identifies this formula where 's' is speed in mph and 'd' is the length of the skid marks in feet?
In the formula s = sqrt(24d) used by traffic investigators to estimate a vehicle's speed before braking, the variable 'd' represents the length of the ____ in feet.
A traffic investigator is using the formula s = sqrt(24d) to estimate the speed of a vehicle involved in a collision. Arrange the following steps in the correct order to calculate the speed (s) based on the measured skid mark length (d).
Traffic accident investigators use the square root formula to reconstruct the events of a crash. Match each component of this formula with the specific real-world value or measurement it represents.
Units of Measurement in Speed Estimation
True or False: In the speed estimation formula , if the product of 24 and the skid mark length () is not a perfect square, the resulting speed () will be an irrational number.
The Mathematical Protocol for Speed Estimation
Forensic Speed Estimation Protocol
In the forensic formula , used by traffic investigators to analyze a crash scene, what does the variable specifically represent?
In a traffic accident investigation, specific mathematical steps are required to utilize the formula . Match each procedural step with its correct description according to the speed estimation protocol.
Learn After
A traffic safety officer is analyzing a 190-foot skid mark using the formula s = sqrt(24d). After substituting the distance into the formula, what is the next mathematical step the officer must perform?
When using the formula s = sqrt(24d) to find the speed of a car that left 190-foot skid marks, the value 190 is substituted for the variable ____.
A traffic investigator is using the formula to determine the speed of a vehicle that left 190-foot skid marks. Arrange the following steps in the correct order to calculate the speed of the car.
A traffic safety investigator is analyzing a 190-foot skid mark to estimate a vehicle's speed. Using the formula , match each numerical value or operation with its correct role in the calculation process.
True or False: When using the formula s = sqrt(24d) for a vehicle that left 190-foot skid marks, the resulting speed is approximately 67.5 mph because the product inside the radical (4,560) is not a perfect square.
Procedural Constraints in Speed Reconstruction
Forensic Audit: 190-Foot Skid Mark Evidence
Professional Reporting of Speed Reconstruction from Skid Marks
After a traffic investigator calculates an estimated speed of 67.5 mph for a 190-foot skid mark, they must verify the result. Which value is substituted back into the formula to check for consistency?
A traffic safety investigator is preparing a report for a vehicle that left 190-foot skid marks. Using the formula , they calculate the speed of the car. In this specific formula, which unit of measurement is the resulting speed () expressed in?