https://file.aiquickdraw.com/mathbot/file/1727468880535r6elnu6l.jpg

The equation in the image represents the centripetal force formula:

\[
F = \frac{mv^2}{r}
\]

where:
- \( F \) is the centripetal force,
- \( m \) is the mass of the object,
- \( v \) is the velocity (with \( v > 0 \)),
- \( r \) is the radius of the circular motion.

The problem asks to solve for \( v \) (velocity).

Let's solve for \( v \):

\[
F = \frac{mv^2}{r}
\]

Multiply both sides by \( r \):

\[
Fr = mv^2
\]

Now, divide both sides by \( m \):

\[
v^2 = \frac{Fr}{m}
\]

Finally, take the square root of both sides to solve for \( v \):

\[
v = \sqrt{\frac{Fr}{m}}
\]

Thus, the velocity \( v \) is:

\[
v = \sqrt{\frac{Fr}{m}}
\]

Would you like more details or have any questions about this? Here are five related questions:

1. How does the mass \( m \) of an object affect its velocity in circular motion?
2. What happens to the velocity if the radius \( r \) increases but the force remains the same?
3. Can this formula be used to describe planetary orbits? If so, how does gravitational force come into play?
4. How do you apply this formula to a practical scenario, such as a car turning in a circular track?
5. What are the units of each quantity involved in this formula?

**Tip:** When dealing with square roots in physics, always consider whether a positive or negative root makes sense for the given context. For velocity, we usually take the positive root as speed is positive.

Solve for velocity (v) from the equation F = mv^2 / r, where F is the centripetal force, m is mass, v is velocity (v > 0), and r is the radius.

Learn how to calculate velocity using the centripetal force formula F = mv^2 / r. This example covers key physics concepts related to circular motion, including algebraic manipulation of the equation to solve for v. Suitable for students in Grades 9-12.

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