To find the radius $r$ of the circular curve, we use the formula for centripetal acceleration:

$a_c = \frac{v^2}{r}$

Where:

• $a_c$ is the centripetal acceleration (6 m/s$^2$),
• $v$ is the velocity (32 m/s),
• $r$ is the radius of the curve (unknown).

Rearranging the formula to solve for $r$:

$r = \frac{v^2}{a_c}$

Substitute the given values:

$r = \frac{(32)^2}{6} = \frac{1024}{6} \approx 170.67 \, \text{m}$

Final Answer:

The radius of the curve is 170.67 meters.

Would you like a detailed explanation of the steps or further clarifications?
Here are 5 related questions to deepen your understanding:

1. What would happen to the radius if Neil's velocity doubled but the centripetal acceleration stayed the same?
2. How would centripetal force relate to the radius if Neil's Ferrari had a given mass?
3. What is the role of friction in providing centripetal force in real-world scenarios like this one?
4. If the centripetal acceleration increased to 12 m/s$^2$ with the same velocity, what would the new radius be?
5. How does centripetal acceleration relate to angular velocity?

Tip: Always ensure units are consistent when solving physics problems to avoid errors in calculations.