Initial angular velocity of a wheel is ` 2 rad//s` .It rotates with a constant angular acceleration of `3.5 rad//s^(2)` .Its angular displacement in 2 s is

Options

A. 4 rad
B. 7 rad
C. 8 rad
D. 11 rad

Explanation

To find the angular displacement of the wheel, we can use the formula for angular displacement under constant angular acceleration:

\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]

Where:
- \(\theta\) is the angular displacement,
- \(\omega_0\) is the initial angular velocity,
- \(t\) is the time,
- \(\alpha\) is the angular acceleration.

### Step 1: Identify the given values
- Initial angular velocity, \(\omega_0 = 2 \, \text{rad/s}\)
- Angular acceleration, \(\alpha = 3.5 \, \text{rad/s}^2\)
- Time, \(t = 2 \, \text{s}\)

### Step 2: Substitute the values into the formula
Now, we substitute the known values into the formula:

\[ \theta = (2 \, \text{rad/s}) \times (2 \, \text{s}) + \frac{1}{2} \times (3.5 \, \text{rad/s}^2) \times (2 \, \text{s})^2 \]

### Step 3: Calculate the first term
Calculate the first term:

\[ \theta_1 = 2 \, \text{rad/s} \times 2 \, \text{s} = 4 \, \text{rad} \]

### Step 4: Calculate the second term
Now calculate the second term:

\[ \theta_2 = \frac{1}{2} \times 3.5 \, \text{rad/s}^2 \times 4 \, \text{s}^2 \]

\[ \theta_2 = \frac{1}{2} \times 3.5 \times 4 = \frac{14}{2} = 7 \, \text{rad} \]

### Step 5: Add the two terms together
Now, add the two angular displacements together:

\[ \theta = \theta_1 + \theta_2 = 4 \, \text{rad} + 7 \, \text{rad} = 11 \, \text{rad} \]

### Final Answer
Thus, the angular displacement of the wheel in 2 seconds is:

\[ \theta = 11 \, \text{rad} \]

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