To determine the speed of the car based on the length of its skid marks, we use the given formula:
[tex]\[
v = \sqrt{20 L}
\][/tex]
where [tex]\( v \)[/tex] represents the speed of the car in miles per hour, and [tex]\( L \)[/tex] is the length of the skid marks in feet.
Here, the length of the skid marks, [tex]\( L \)[/tex], is measured to be 195 feet. We substitute this value into the formula to find the speed.
First, substitute [tex]\( L = 195 \)[/tex] into the formula:
[tex]\[
v = \sqrt{20 \times 195}
\][/tex]
Calculate the product inside the square root:
[tex]\[
20 \times 195 = 3900
\][/tex]
Now, we take the square root of 3900:
[tex]\[
v = \sqrt{3900}
\][/tex]
By evaluating the square root of 3900, we get:
[tex]\[
v = 62.44997998398398
\][/tex]
Next, we round this value to the nearest tenth. The digit in the hundredths place is 4, which is less than 5, so we round down the digit in the tenths place:
[tex]\[
v \approx 62.4
\][/tex]
Thus, the estimated speed of the car at the time it started braking, based on the length of the skid marks, is approximately 62.4 miles per hour.
