A point on the rim of a disc starts circular motion from rest and after time t, it gains an angular acceleration given by `alpha=3t-t^(2)`. Calculate the angular velocity after 2 s.

Explanation

To solve the problem step by step, we will follow the process of integrating the given angular acceleration to find the angular velocity after 2 seconds.

### Step 1: Understand the given information
- The initial angular velocity, \( \omega_0 = 0 \) rad/s (since the motion starts from rest).
- The angular acceleration is given by \( \alpha(t) = 3t - t^2 \).

### Step 2: Relate angular acceleration to angular velocity
We know that angular acceleration \( \alpha \) is the rate of change of angular velocity \( \omega \) with respect to time \( t \):
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