An automobile crash investigator measured the skid marks of one of the vehicles involved in a crash. The length of the skid marks was 85 feet. Use the formula [tex]$s=\sqrt{24 d}$[/tex], where [tex]$s$[/tex] is the speed of the vehicle, in miles per hour, before the brakes were applied, and [tex]$d$[/tex] is the length of the skid marks, in feet, to find the speed of the vehicle before it started braking. Round your answer to the nearest tenth.

Answer: [ ] miles per hour

Question

An automobile crash investigator measured the skid marks of one of the vehicles involved in a crash. The length of the skid marks was 85 feet. Use the formula [tex]$s=\sqrt{24 d}$[/tex], where [tex]$s$[/tex] is the speed of the vehicle, in miles per hour, before the brakes were applied, and [tex]$d$[/tex] is the length of the skid marks, in feet, to find the speed of the vehicle before it started braking. Round your answer to the nearest tenth. 
 
Answer: [ ] miles per hour

GinnyAnswer · Answer

Substitute the given value of d = 85 into the formula s = ". s q r t 24 d " . 
 Calculate the value of s = ". s q r t 24 × 85 " = ". s q r t 2040 " . 
 Find the square root: s ≈ 45.166 . 
 Round to the nearest tenth: s ≈ 45.2 ​ miles per hour. 
 
 Explanation 
 
 Understanding the Problem We are given the formula s = ". s q r t 24 d " which relates the speed of a vehicle ( s ) to the length of its skid marks ( d ). We are given that the length of the skid marks is 85 feet, so d = 85 . We need to find the speed s and round it to the nearest tenth. 
 
 Substituting the Value of d Substitute d = 85 into the formula: s = ". s q r t 24 × 85 " s = ". s q r t 2040 " 
 
 Calculating the Square Root Calculate the square root of 2040. The result of this operation is approximately 45.166. 
 
 Rounding to the Nearest Tenth Round the result to the nearest tenth. Since the hundredths digit is 6, which is greater than or equal to 5, we round up the tenths digit. Thus, 45.166 rounded to the nearest tenth is 45.2. 
 
 Final Answer Therefore, the speed of the vehicle before it started braking was approximately 45.2 miles per hour.

Examples 
 Understanding the relationship between skid mark length and vehicle speed is crucial in accident investigation. For instance, if an accident occurs and the skid marks are measured to be 100 feet long, using the formula s = ". s q r t 24 d " , we can estimate the vehicle's speed before braking. This information helps investigators determine if the driver was speeding or if other factors contributed to the accident. This calculation provides a basis for further analysis and helps reconstruct the events leading up to the collision.

Answer (1)

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