https://file.aiquickdraw.com/mathbot/file/1730493336230j1njw846.jpg

To solve this problem, we need to find the centripetal acceleration of a car moving in a circular path with a given radius and speed.

### Given:
- Radius \( r = 19.0 \, \text{m} \)
- Speed \( v = 9.87 \, \text{m/s} \)

### Formula for Centripetal Acceleration
The centripetal acceleration \( a_c \) is given by the formula:
\[
a_c = \frac{v^2}{r}
\]

### Calculation
1. Substitute the values:
   \[
   a_c = \frac{(9.87)^2}{19.0}
   \]

2. Calculate \( 9.87^2 \):
   \[
   9.87^2 = 97.4169
   \]

3. Now divide by the radius:
   \[
   a_c = \frac{97.4169}{19.0} \approx 5.13 \, \text{m/s}^2
   \]

### Answer
The centripetal acceleration is approximately:
\[
a_c \approx 5.13 \, \text{m/s}^2
\]

Would you like further details or have any other questions?

### Related Questions
1. What would be the centripetal acceleration if the radius of the turn was doubled?
2. How does the centripetal force relate to centripetal acceleration in this scenario?
3. What is the role of friction in maintaining this centripetal force on flat ground?
4. How would the acceleration change if the speed of the car was halved?
5. What would happen to the required centripetal force if the car's mass was doubled?

### Tip
Centripetal acceleration always points toward the center of the circular path, keeping the object in circular motion.

A car makes a 19.0 m radius turn at 9.87 m/s on flat ground. What is its centripetal acceleration?

Find the centripetal acceleration of a car making a 19.0 m radius turn at 9.87 m/s on flat ground. This solution explores concepts of circular motion and centripetal acceleration, using the formula a_c = v^2 / r. Suitable for high school physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation