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seja o raio da circunferência 30cm, e a reta que liga A e B o diâmetro

The problem is about a train moving from point A to point B, where the average speed is represented by \( r_m \) and the magnitude of the average velocity is represented by \( v_m \). We are tasked with determining the correct relationship between these two quantities.

The additional information you provided mentions that the path between A and B can be visualized as a circumference, with the distance between A and B being the diameter.

Let’s break down the problem:

1. **Average speed (\( r_m \))** is the total distance traveled by the train along its path. Since the train is traveling along the circumference, this is the perimeter of a semicircle. If the radius of the circle is given as 30 cm, the perimeter of the semicircular path is:
   \[
   \text{Perimeter of semicircle} = \pi \times \text{radius} = \pi \times 30 \, \text{cm} = 30\pi \, \text{cm}.
   \]
   
2. **Average velocity (\( v_m \))** is the straight-line distance between the initial and final points, which is the diameter of the circle:
   \[
   \text{Diameter} = 2 \times \text{radius} = 2 \times 30 \, \text{cm} = 60 \, \text{cm}.
   \]

Now, to find the ratio \( \frac{r_m}{v_m} \):

\[
\frac{r_m}{v_m} = \frac{30\pi}{60} = \frac{\pi}{2}.
\]

So, the correct answer is **Option A**:
\[
\frac{r_m}{v_m} = \frac{\pi}{2}.
\]

Would you like further clarification on any part of this explanation?

### Here are 5 related questions:
1. How would the result change if the path was a full circle instead of a semicircle?
2. What is the difference between speed and velocity in terms of their definitions?
3. How can the concept of average speed apply to a non-circular path?
4. Why is the average velocity based on displacement, not the total path length?
5. What would be the ratio \( \frac{r_m}{v_m} \) if the train moved along a quarter of the circle?

### Tip:
Remember, **speed** is a scalar quantity representing how fast an object moves, while **velocity** is a vector that also includes direction.

Considere que o comboio se desloca de A para B. Sendo a rapidez média representada por r_m e o módulo da velocidade média por v_m, é correto afirmar que neste percurso r_m / v_m = ?

This problem involves determining the relationship between average speed and average velocity for a train moving along a circular path. The solution involves key formulas related to circular motion and distance vs. displacement. Suitable for high school students (Grades 9-11).

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