A particle starts from rest and its angular displacement (in rad) is given `theta=(t^2)/(20)+t/5`. Calculate the angular velocity at the end of `t=4s`.

Explanation

To solve the problem, we need to calculate the angular velocity of the particle at the end of \( t = 4 \) seconds, given the angular displacement equation:

\[ \theta = \frac{t^2}{20} + \frac{t}{5} \]

### Step 1: Differentiate the angular displacement with respect to time
The angular velocity \( \omega \) is defined as the rate of change of angular displacement \( \theta \) with respect to time \( t \). Therefore, we differentiate \( \theta \):
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