Starting from rest, a wheel has constant `alpha=3.0rad//s^(2)`. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval?

Explanation

To solve the problem, we need to use the equations of motion for rotational dynamics. We are given the following information:

- The angular acceleration, \( \alpha = 3.0 \, \text{rad/s}^2 \)
- The angular displacement during the 4-second interval, \( \Delta \theta = 120 \, \text{rad} \)
- The initial angular velocity, \( \omega_0 = 0 \, \text{rad/s} \) (since it starts from rest)

We need to find the time \( t_1 \) it took to reach the 4-second interval \( t_2 \).

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