To calculate the radius of the curve, we use the formula for centripetal acceleration:

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

Where:

• $a_c$ is the centripetal acceleration ($7 \, \text{m/s}^2$),
• $v$ is the velocity ($29 \, \text{m/s}$),
• $r$ is the radius of the curve (to be calculated).

Rearranging the formula to solve for $r$:

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

Substituting the known values:

$r = \frac{29^2}{7}$

$r = \frac{841}{7}$

$r = 120.14 \, \text{m}$

Final Answer:

The radius of the curve is 120.14 meters.

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Would you like further explanation or have any questions? Here are some related queries you might explore:

1. What happens to the radius if the velocity increases but acceleration stays constant?
2. How is centripetal force related to centripetal acceleration?
3. If Neil’s car has a mass of 1,500 kg, what is the centripetal force acting on it?
4. How does the coefficient of friction affect driving on a curve?
5. What are some real-life examples of centripetal force applications?

Tip: Remember that centripetal acceleration always points toward the center of the curve in circular motion.