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Answer :
To solve the problem of estimating the speed of a vehicle before the brakes were applied, we use the formula:
[tex]\[ 0.75 \times d = \frac{s^2}{30.25} \][/tex]
where:
- [tex]\( s \)[/tex] is the speed in miles per hour,
- [tex]\( d \)[/tex] is the length of the skid marks in feet.
Given that the skid mark [tex]\( d \)[/tex] measures 90 feet, we'll find the speed [tex]\( s \)[/tex].
1. Substitute the known value into the formula:
[tex]\[ 0.75 \times 90 = \frac{s^2}{30.25} \][/tex]
2. Multiply to solve for [tex]\( s^2 \)[/tex]:
[tex]\[ 0.75 \times 90 = 67.5 \][/tex]
Now, substitute this into the equation:
[tex]\[ 67.5 = \frac{s^2}{30.25} \][/tex]
3. Solve for [tex]\( s^2 \)[/tex]:
To isolate [tex]\( s^2 \)[/tex], multiply both sides by 30.25:
[tex]\[ s^2 = 67.5 \times 30.25 = 2041.875 \][/tex]
4. Find [tex]\( s \)[/tex] by taking the square root:
[tex]\[ s = \sqrt{2041.875} \][/tex]
Calculating this gives us:
[tex]\[ s \approx 45.19 \][/tex]
Thus, the approximate speed of the vehicle before the brakes were applied was 45.19 miles per hour.
[tex]\[ 0.75 \times d = \frac{s^2}{30.25} \][/tex]
where:
- [tex]\( s \)[/tex] is the speed in miles per hour,
- [tex]\( d \)[/tex] is the length of the skid marks in feet.
Given that the skid mark [tex]\( d \)[/tex] measures 90 feet, we'll find the speed [tex]\( s \)[/tex].
1. Substitute the known value into the formula:
[tex]\[ 0.75 \times 90 = \frac{s^2}{30.25} \][/tex]
2. Multiply to solve for [tex]\( s^2 \)[/tex]:
[tex]\[ 0.75 \times 90 = 67.5 \][/tex]
Now, substitute this into the equation:
[tex]\[ 67.5 = \frac{s^2}{30.25} \][/tex]
3. Solve for [tex]\( s^2 \)[/tex]:
To isolate [tex]\( s^2 \)[/tex], multiply both sides by 30.25:
[tex]\[ s^2 = 67.5 \times 30.25 = 2041.875 \][/tex]
4. Find [tex]\( s \)[/tex] by taking the square root:
[tex]\[ s = \sqrt{2041.875} \][/tex]
Calculating this gives us:
[tex]\[ s \approx 45.19 \][/tex]
Thus, the approximate speed of the vehicle before the brakes were applied was 45.19 miles per hour.
Thank you for reading the article Police can estimate the speed of a vehicle before the brakes are applied using the formula tex 0 75d frac s 2 30 25 tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
