A child was struck by a car in a crosswalk. The driver of the car had slammed on his brakes and left visible skid marks on the pavement. He told the police he had been driving at

20

miles per hour. If the man is telling the truth, how long should the skid marks be? Do not round.

If the driver was telling the truth, the skid marks should be how many feet long.

To solve this problem, we need to use the physics formula that relates the stopping distance (skid mark length), initial speed, and deceleration.

The formula is:

\[
d = \frac{v^2}{2a}
\]

Where:
- \(d\) is the stopping distance (length of skid marks).
- \(v\) is the initial velocity of the car.
- \(a\) is the deceleration due to braking (typically the acceleration due to gravity multiplied by the coefficient of friction).

We'll need to use consistent units, so first, let's convert the speed from miles per hour to feet per second.

### Step 1: Convert 20 miles per hour to feet per second.

\[
1 \text{ mile} = 5280 \text{ feet}
\]
\[
1 \text{ hour} = 3600 \text{ seconds}
\]

Thus:
\[
v = 20 \times \frac{5280}{3600} = 29.33 \text{ feet per second}
\]

### Step 2: Use a typical coefficient of friction for dry asphalt.
The coefficient of friction between rubber tires and dry asphalt is typically around \( \mu = 0.7 \). The deceleration \(a\) is then:

\[
a = \mu g = 0.7 \times 32.2 \text{ ft/s}^2 = 22.54 \text{ ft/s}^2
\]

### Step 3: Calculate the skid mark distance.

Now substitute the values into the equation \( d = \frac{v^2}{2a} \):

\[
d = \frac{(29.33)^2}{2 \times 22.54} = \frac{860.35}{45.08} \approx 19.08 \text{ feet}
\]

Thus, if the driver was telling the truth, the skid marks should be about **19.08 feet** long.

Would you like more details or have any questions?

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**Related Questions:**
1. How does the length of skid marks change if the car was traveling faster?
2. What happens to the skid mark length if the road is wet?
3. How would the skid marks be affected if the coefficient of friction was 0.5 instead of 0.7?
4. What role does the weight of the car play in determining the skid mark length?
5. How would the stopping distance change if the driver delayed braking by 1 second?

**Tip:** Always ensure that units are consistent when performing calculations, especially in physics problems!

A child was struck by a car in a crosswalk. The driver of the car had slammed on his brakes and left visible skid marks on the pavement. He told the police he had been driving at 20 miles per hour. If the man is telling the truth, how long should the skid marks be? Do not round. If the driver was telling the truth, the skid marks should be how many feet long.

Learn how to calculate the skid mark length left by a car traveling at 20 miles per hour using the formula d = v^2 / 2a. This problem covers key concepts in kinematics, friction, and deceleration, suitable for students in Grades 9-12. A typical coefficient of friction for dry asphalt is applied in the calculation, yielding a skid mark length of approximately 19.08 feet.

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