A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{{{\pi }^{2}}}{2}\]
D) \[\frac{{{\pi }^{2}}}{4}\]
Correct Answer: C
Solution :
Given:\[x=2\cos \left( 0.5\pi t+\frac{\pi }{3} \right)\] \[\therefore \]velocity \[V=\frac{dx}{dt}=2\times 0.5\pi \sin \left( 0.5\pi t+\frac{\pi }{3} \right)\] \[\therefore \]Acceleration\[a=\frac{dV}{dt}=-2\times 0.5\pi \times 0.5\pi \cos \left( 0.5\pi t+\frac{\pi }{3} \right)\] \[\therefore \]Max. acceleration \[{{a}_{mix}}=-2\times 0.5\pi \times 0.5\pi =-\frac{{{\pi }^{2}}}{2}cm/{{s}^{2}}\] \[\therefore \]Magnitude is \[\left| {{a}_{\max }} \right|=\left| -\frac{{{\pi }^{2}}}{2} \right|=\frac{{{\pi }^{2}}}{2}cm/{{s}^{2}}\] Hence, the correction option is (c).
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