A rear-end collision that involved a motorcycle hitting the rear of a Toktok happened along Diosdado Macapagal National Highway in Brgy. Matiao, City of Mati. According to witnesses, the motorcycle was travelling very fast but according to the driver, he was just travelling at 30km/h along the dry, asphalted road when the accident happened, leaving two (2) skid marks, each measuring 25 feet, on the road surface.   Solve for the speed of the driver based on the length of the 2 skid marks and the dry, asphalted road

To determine the actual speed of the motorcycle based on the length of the skid marks, we can use a formula derived from physics and accident reconstruction known as the **skid speed formula**. This formula takes into account the length of the skid marks, the drag factor of the road surface, and the braking efficiency of the vehicle.

### Skid Speed Formula:
\[
v = \sqrt{2 \cdot f \cdot d \cdot 9.8}
\]

Where:
- \(v\) is the speed of the vehicle in meters per second (m/s),
- \(f\) is the **drag factor** of the road surface (for dry asphalt, \(f\) typically ranges from 0.6 to 0.8),
- \(d\) is the **length of the skid marks** in meters,
- \(9.8 \, \text{m/s}^2\) is the acceleration due to gravity.

### Given dataTo determine the actual speed of the motorcycle based on the length of the skid marks, we can use a formula derived from physics and accident reconstruction known as the **skid speed formula**. This formula takes into account the length of the skid marks, the drag factor of the road surface, and the braking efficiency of the vehicle.

### Skid Speed Formula:
\[
v = \sqrt{2 \cdot f \cdot d \cdot 9.8}
\]

Where:
- \(v\) is the speed of the vehicle in meters per second (m/s),
- \(f\) is the **drag factor** of the road surface (for dry asphalt, \(f\) typically ranges from 0.6 to 0.8),
- \(d\) is the **length of the skid marks** in meters,
- \(9.8 \, \text{m/s}^2\) is the acceleration due to gravity.

### Given 
- The length of the skid marks is 25 feet per mark, so the total length \(d\) is \(25 \, \text{feet} = 7.62 \, \text{meters}\).
- The drag factor for a dry asphalt road \(f\) is assumed to be 0.7 (a typical value).

### Step 1: Convert the skid mark length to meters
Since 1 foot = 0.3048 meters,
\[
d = 25 \, \text{feet} = 25 \times 0.3048 = 7.62 \, \text{meters}.
\]

### Step 2: Plug values into the skid speed formula
Using \(f = 0.7\), \(d = 7.62 \, \text{meters}\), and \(g = 9.8 \, \text{m/s}^2\):
\[
v = \sqrt{2 \cdot 0.7 \cdot 7.62 \cdot 9.8}
\]
Let me calculate that.

The speed of the motorcycle at the time of the accident, based on the skid marks, is approximately \( 10.22 \, \text{m/s} \).

To convert this into kilometers per hour (km/h):
\[
v_{\text{km/h}} = v_{\text{m/s}} \times 3.6
\]
\[
v_{\text{km/h}} = 10.22 \times 3.6 \approx 36.8 \, \text{km/h}
\]

Thus, the motorcycle was traveling at approximately **36.8 km/h**, which is faster than the 30 km/h stated by the driver.

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Would you like to dive deeper into any aspect of this calculation or have further clarifications?

### Related questions:
1. What factors affect the drag coefficient on different road surfaces?
2. How do weather conditions impact the length of skid marks?
3. How is braking efficiency considered in accidents involving different types of vehicles?
4. Can the skid speed formula be applied to other types of accidents, like car-on-car collisions?
5. How accurate is the skid mark analysis in determining speed in real-world situations?

**Tip**: Always ensure your tire condition is good to reduce skid lengths and maintain road safety.

A rear-end collision that involved a motorcycle hitting the rear of a Toktok happened along Diosdado Macapagal National Highway in Brgy. Matiao, City of Mati. According to witnesses, the motorcycle was travelling very fast but according to the driver, he was just travelling at 30km/h along the dry, asphalted road when the accident happened, leaving two (2) skid marks, each measuring 25 feet, on the road surface. Solve for the speed of the driver based on the length of the 2 skid marks and the dry, asphalted road.

Solve for the speed of a motorcycle involved in a rear-end collision based on the length of two skid marks (25 feet each) on a dry asphalt road. Using the skid speed formula, the solution demonstrates how to calculate the actual speed at the time of the accident. Suitable for physics students in Grades 10-12.

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