An object is moving in a circle of radius 100 m with a constant speed of `31.4 m//s` . What is its average speed for one complete revolution

Options

A. Zero
B. `31.4 m//s`
C. `3.14m//s`
D. `sqrt(2) xx 31.4 m//s`

Answer

To find the average speed of an object moving in a circle with a constant speed, we can follow these steps:

### Step 1: Understand the Problem
We know that the object is moving in a circular path with a radius of 100 meters and a constant speed of 31.4 m/s. We need to determine the average speed for one complete revolution.

### Step 2: Calculate the Circumference of the Circle
The distance traveled in one complete revolution (which is the circumference of the circle) can be calculated using the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

Substituting the given radius:
\[ C = 2 \times \pi \times 100 \, \text{m} = 200\pi \, \text{m} \approx 628.32 \, \text{m} \]

### Step 3: Calculate the Time for One Complete Revolution
Next, we need to find the time taken to complete one revolution. This can be calculated using the formula:
\[ T = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the circumference we just calculated, and the speed is given as 31.4 m/s.

Substituting the values:
\[ T = \frac{200\pi \, \text{m}}{31.4 \, \text{m/s}} \approx \frac{628.32 \, \text{m}}{31.4 \, \text{m/s}} \approx 20 \, \text{s} \]

### Step 4: Calculate the Average Speed
The average speed is defined as the total distance traveled divided by the total time taken. Since the object travels the circumference of the circle in one complete revolution, we can use the formula:
\[ V_{\text{average}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{C}{T} \]

Substituting the values we calculated:
\[ V_{\text{average}} = \frac{200\pi \, \text{m}}{20 \, \text{s}} = 10\pi \, \text{m/s} \approx 31.4 \, \text{m/s} \]

### Conclusion
The average speed for one complete revolution is approximately 31.4 m/s.

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