A) \[a\,\,\theta \,\,\cos \theta \]
B) \[a\,\omega \]
C) \[a\,\omega \,\sin \theta \]
D) none of these
Correct Answer: C
Solution :
Given equation of motion is \[x=a\,\cos (\omega t-\theta )\] ......(i) differentiate equation (i) with respect to, t, we get, \[\frac{dx}{dt}=-a\omega \,\sin \,(\omega t-\theta )\] \[(\therefore \,\frac{d}{dt}\,\cos \,(\omega t-\theta )=-\omega \,\sin \,(\omega t-\theta )\] Hence, velocity \[\left| \frac{dx}{dt} \right|=a\omega \,\sin (\omega t-\theta )\] If \[(\omega t-\theta ){{90}^{o}},\] the velocity will be = 1 (maximum value) Thus the maximum velocity is \[V=a\omega .\]
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