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Q.
A particle starts from rest and its angular displacement (in radians) is given by $\theta =\frac{t^{2}}{20}+\frac{t}{5} .$ If the angular velocity at the end of $t =4$ is $k$, then the value of $5\, k$ is
$\frac{ d \theta}{ dt }=\frac{2 t }{20}+\frac{1}{5}$
$=\frac{ t }{10}+\frac{1}{5}$
$\left(\frac{ d \theta}{ dt }\right)_{\varepsilon=4}=\frac{4}{10}+\frac{1}{5}$
$k =\frac{3}{5}$
$5 k =3$