A wheel starting from rest is uniformly accelerated at `4rad//s^(2)` for `10s`. It is allowed to rotated uniformly for the next 10 s and is finally brought to rest in the next 10 s. Find the total angle rotated by the wheel.

Explanation

To solve the problem step by step, we will analyze the motion of the wheel in three distinct phases: uniform acceleration, uniform motion, and uniform deceleration.

### Step 1: Uniform Acceleration
1. **Initial Conditions**: The wheel starts from rest, so the initial angular velocity (\( \omega_i \)) is \( 0 \, \text{rad/s} \).
2. **Angular Acceleration**: The wheel is uniformly accelerated at \( \alpha = 4 \, \text{rad/s}^2 \).
3. **Time of Acceleration**: The time for which the wheel accelerates is \( t = 10 \, \text{s} \).

Using the formula for final angular velocity:
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