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The provided function is:

\[
S = \sqrt{30d}
\]

Where:
- \( S \) is the speed of the car in miles per hour.
- \( d \) is the distance in feet that the car skids after applying the brakes.

You are asked to estimate the speed \( S \) of a car that leaves an 80-foot-long skid mark, so we substitute \( d = 80 \) into the equation:

\[
S = \sqrt{30 \times 80}
\]

Let's calculate that.The estimated speed of the car is approximately 49 miles per hour when it leaves an 80-foot-long skid mark. 

Would you like further details or explanations on this calculation?

Here are 5 related questions to explore:
1. How would the speed change if the skid mark length were doubled?
2. What is the physical significance of the constant 30 in this equation?
3. Can this formula be applied to wet or icy road conditions?
4. How would you calculate the distance if the speed is known?
5. What assumptions does this model make about braking and road conditions?

**Tip:** Always ensure the units used in formulas match the context (e.g., feet, miles, or meters). Misalignment can lead to significant errors in calculations!

Use a calculator to estimate the speed of a car that leaves 80-foot-long skid marks on a dry tar road, using the function S = √(30d).

Learn how to estimate the speed of a car that leaves 80-foot-long skid marks using the function S = √(30d). This problem covers square roots and speed-distance relationships, ideal for students in Grades 9-12.

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