question_answer

An athlete completes one round of a circular track of radius R in 40 seconds. What will be the displacement at the end of 2 min. 20 second?

Answer:

                The value of displacement x will be maximum, when the value of \[\text{ sin}\left( \omega t+\theta  \right)\]is maximum. It will be so if \[\text{ sin}\left( \omega t+\theta  \right)=1=\sin \pi /2\]or\[\omega t+\theta =\frac{\pi }{2}\]or\[\omega t=\frac{\pi }{2}-\theta \]                               \[\therefore \]  \[t=\left( \frac{\pi }{2\omega }-\frac{\theta }{\omega } \right)\]