A) \[\frac{\sqrt{3}A\omega }{2}\]
B) \[\frac{\sqrt{3}A\omega }{4}\]
C) \[\frac{3A\omega }{\pi }\]
D) \[\frac{3A\omega }{\pi }(2-\sqrt{3})\]
Correct Answer: D
Solution :
[d] Average velocity \[\bar{v}=\frac{\int\limits_{0}^{t}{\frac{dx}{dt}.dt}}{t}=\frac{\int\limits_{0}^{t}{dx}}{t}=\frac{x(t)-x(0)}{t}\] \[=\frac{A(cos\pi /6-1)}{\pi /6\omega }=\frac{3A\omega }{\pi }(\sqrt{3}-2)\] Since particle does not change its direction in the given interval, average speed becomes \[\left| {\bar{v}} \right|=\frac{3A\omega }{\pi }(2-\sqrt{3})\]
You need to login to perform this action.
You will be redirected in
3 sec
