A particle starts from rest and moves on a curve with constant angular acceleration of `3.0 rad//s^(2)`. An observer starts his stopwatch at a certain instant and recond that the particle covers an angular span of `120` rad at the end of `4^(th)` second. How long the particle has moved when the observer started his stopwatch?

Explanation

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the Problem
We have a particle that starts from rest and moves with a constant angular acceleration of \(3.0 \, \text{rad/s}^2\). An observer starts timing when the particle has covered an angular displacement of \(120 \, \text{rad}\) at the end of the \(4^{th}\) second. We need to find out how long the particle has been moving when the observer starts the stopwatch.

### Step 2: Identify Known Values
- Initial angular velocity, \( \omega_0 = 0 \, \text{rad/s} \) (since it starts from rest)
- Angular acceleration, \( \alpha = 3.0 \, \text{rad/s}^2 \)
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