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  4. If the equation for the displacement of a particle moving on a circular path is given by θ =2t3+0.5, where θ is in radian and t in second, then the angular velocity of the particle after 2 s from its start is

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Q. If the equation for the displacement of a particle moving on a circular path is given by $ \theta =2{{t}^{3}}+0.5, $ where $ \theta $ is in radian and t in second, then the angular velocity of the particle after 2 s from its start is

MGIMS WardhaMGIMS Wardha 2014

Solution:

Since, $ \theta =2{{t}^{3}}+0.5, $ the angular velocity of the particle $ =\frac{d\theta }{dt}=6{{t}^{2}}, $ At $ t=2\text{ }s, $ angular velocity $ =6\times 22=24\text{ }rad/s $