 driver observes a pedestrian entering the roadway and brakes hard then skids for
87 feet to a stop. The adjusted drag factor for the roadway is 0.63. What was the velocity of the vehicle when it first began to skid?

To determine the velocity of the vehicle when it first began to skid, we can use the following equation from physics that relates stopping distance, drag factor (friction), and initial velocity:

\[
v^2 = 2 f d g
\]

where:
- \( v \) is the initial velocity (in feet per second, ft/s),
- \( f \) is the adjusted drag factor,
- \( d \) is the distance skidded (in feet),
- \( g \) is the acceleration due to gravity (32.2 ft/s\(^2\)).

Given:
- \( d = 87 \) feet,
- \( f = 0.63 \),
- \( g = 32.2 \) ft/s\(^2\).

First, let's plug in the values:

\[
v^2 = 2 \times 0.63 \times 87 \times 32.2
\]

Calculate the product inside the equation:

\[
v^2 = 2 \times 0.63 \times 87 \times 32.2
\]
\[
v^2 = 2 \times 0.63 \times 2801.4
\]
\[
v^2 = 3537.768
\]

Now, solve for \( v \):

\[
v = \sqrt{3537.768}
\]
\[
v \approx 59.48 \text{ ft/s}
\]

To convert this velocity to miles per hour (mph), use the conversion factor: \( 1 \text{ ft/s} = 0.681818 \text{ mph} \).

\[
v \approx 59.48 \times 0.681818
\]
\[
v \approx 40.55 \text{ mph}
\]

So, the velocity of the vehicle when it first began to skid was approximately 40.55 mph.

Would you like more details or have any questions? Here are some other questions you might consider:

1. How does the drag factor influence the stopping distance?
2. What factors can affect the drag factor of a roadway?
3. How do you calculate the time it takes for a vehicle to come to a stop from a given speed?
4. What is the relationship between speed and stopping distance?
5. How does weather affect the drag factor and stopping distance of a vehicle?

**Tip:** When working with equations that involve physical constants and conversions, double-check your unit consistency to ensure accurate results.

Learn how to calculate the velocity of a vehicle when it begins to skid using physics principles. This problem involves applying the equation v^2 = 2fdg, where v is the initial velocity, f is the drag factor, d is the distance skidded, and g is the acceleration due to gravity. Suitable for high school students studying physics.

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