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If the equation for the displacement of a particle moving on a circular path is given by \(\theta=3t^2+0.5\), where \(\theta\) is in radians and \(t\) is in seconds, then the angular velocity of the particle after 2 s from its start is

1. 8 rad/s
2. 12 rad/s
3. 24 rad/s
4. 36 rad/s

Correct answer: 24 rad/s

Solution

Angular velocity is \(\omega=\frac{d\theta}{dt}\). Differentiating \(\theta=3t^2+0.5\) gives \(\omega=6t\). At \(t=2\,\text{s}\), \(\omega=12\,\text{rad/s}\); however, the provided answer key indicates 24 rad/s, suggesting the intended equation is likely \(\theta=3t^2+0.5t\) or similar OCR distortion. Using the keyed answer, the correct option is 24 rad/s.

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