An automobile crash investigator measured the skid marks of one of the vehicles involved in a crash. The length of the skid marks was 157 feet. Use the formula [tex]$8=\sqrt{24 d}$[/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 (1)
Substitute the given skid mark length d = 157 feet into the formula s = 24 d .
Calculate the square root: s = 24 × 157 = 3768 ≈ 61.384 .
Round the result to the nearest tenth: s ≈ 61.4 .
The speed of the vehicle before braking is 61.4 miles per hour.
Explanation
Understanding the Problem We are given the formula s = 24 d , where s is the speed of the vehicle in miles per hour and d is the length of the skid marks in feet. We are also given that the length of the skid marks is 157 feet, so d = 157 . Our goal is to find the speed s of the vehicle before it started braking.
Substituting the Value of d Substitute the given value of d into the formula: s = 24 × 157
Calculating the Square Root Calculate the value of s :
s = 3768 s ≈ 61.384
Rounding to the Nearest Tenth Round the calculated value of s to the nearest tenth: s ≈ 61.4
Final Answer Therefore, the speed of the vehicle before it started braking was approximately 61.4 miles per hour.
Examples
Understanding the relationship between skid mark length and vehicle speed is crucial in accident reconstruction. For example, if an accident occurs and the skid marks are measured to be 200 feet long, we can use the formula to estimate the vehicle's speed before braking. This information can help determine if the driver was speeding or driving recklessly, which is vital for legal and insurance purposes. By applying this formula, investigators can piece together the events leading up to the crash and ensure accountability.
