Question
A car traveling at 60 miles per hour needs to stop within 100 meters to avoid hitting an object.
Answers
GPT-4o mini
To determine whether a car traveling at 60 miles per hour can stop within 100 meters, we need to convert the speed from miles per hour to meters per second and then calculate the stopping distance based on typical deceleration rates.
1. **Convert Speed to Meters per Second:**
\( 60 \text{ miles/hour} = 60 \times 1609.34 \text{ meters}/3600 \text{ seconds} \approx 26.82 \text{ meters/second} \)
2. **Use the Stopping Distance Formula:**
The stopping distance \( d \) can be calculated using the formula:
\[
d = \frac{v^2}{2a}
\]
where:
- \( v \) is the initial velocity (in meters per second)
- \( a \) is the deceleration (in meters per second squared)
3. **Estimate Deceleration:**
A typical deceleration for a car on dry pavement can range from \( 6 \, \text{m/s}^2 \) to \( 10 \, \text{m/s}^2 \). We can use \( 8 \, \text{m/s}^2 \) as a reasonable estimate for this calculation.
4. **Calculate Stopping Distance:**
Plugging the numbers into the formula:
\[
d = \frac{(26.82)^2}{2 \times 8}
\]
\[
d = \frac{718.5924}{16} \approx 44.91 \text{ meters}
\]
5. **Comparison with Required Stopping Distance:**
The stopping distance calculated (approximately 44.9 meters) is much less than the 100 meters required to avoid hitting an object. Thus, the car can indeed stop within the required distance.
In conclusion, a car traveling at 60 miles per hour can stop within 100 meters given reasonable assumptions about deceleration.
1. **Convert Speed to Meters per Second:**
\( 60 \text{ miles/hour} = 60 \times 1609.34 \text{ meters}/3600 \text{ seconds} \approx 26.82 \text{ meters/second} \)
2. **Use the Stopping Distance Formula:**
The stopping distance \( d \) can be calculated using the formula:
\[
d = \frac{v^2}{2a}
\]
where:
- \( v \) is the initial velocity (in meters per second)
- \( a \) is the deceleration (in meters per second squared)
3. **Estimate Deceleration:**
A typical deceleration for a car on dry pavement can range from \( 6 \, \text{m/s}^2 \) to \( 10 \, \text{m/s}^2 \). We can use \( 8 \, \text{m/s}^2 \) as a reasonable estimate for this calculation.
4. **Calculate Stopping Distance:**
Plugging the numbers into the formula:
\[
d = \frac{(26.82)^2}{2 \times 8}
\]
\[
d = \frac{718.5924}{16} \approx 44.91 \text{ meters}
\]
5. **Comparison with Required Stopping Distance:**
The stopping distance calculated (approximately 44.9 meters) is much less than the 100 meters required to avoid hitting an object. Thus, the car can indeed stop within the required distance.
In conclusion, a car traveling at 60 miles per hour can stop within 100 meters given reasonable assumptions about deceleration.