Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at `9.1 "rad"//s`. The wheel has a radius of 0.45 m. If you ride the bike for 35 min, how far would you have gone if the bike could move?

Options

A. 3900 m
B. 7800 m
C. 4300 m
D. 8600 m

Explanation

To solve the problem step by step, we will first convert the angular speed from radians per second to a linear distance traveled over the given time.

### Step 1: Convert angular speed to linear speed
The angular speed of the wheel is given as \( \omega = 9.1 \, \text{rad/s} \). The linear speed \( v \) can be calculated using the formula:
\[ v = r \cdot \omega \]
where \( r \) is the radius of the wheel.

Given:
- \( r = 0.45 \, \text{m} \)
- \( \omega = 9.1 \, \text{rad/s} \)

Substituting the values:
\[ v = 0.45 \, \text{m} \cdot 9.1 \, \text{rad/s} = 4.095 \, \text{m/s} \]

### Step 2: Convert time from minutes to seconds
The time given is \( 35 \, \text{minutes} \). We need to convert this into seconds:
\[ t = 35 \, \text{minutes} \times 60 \, \text{seconds/minute} = 2100 \, \text{seconds} \]

### Step 3: Calculate the distance traveled
The distance \( d \) traveled can be calculated using the formula:
\[ d = v \cdot t \]

Substituting the values:
\[ d = 4.095 \, \text{m/s} \cdot 2100 \, \text{s} = 8600.5 \, \text{m} \]

### Final Answer
If the bike could move, you would have gone approximately \( 8600.5 \, \text{m} \) or \( 8.6 \, \text{km} \).

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