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Question

The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as
x=2 cos(0.5πt+π3)
The magnitude of the maximum acceleration of the particle in cms2 is


A

π2

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B

π4

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C

π22

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D

π24

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Solution

The correct option is C

π22


Given that, x=2 cos(0.5πt+π3)
Velocity, v=dxdt=2×0.5π sin(0.5πt+π3)
and acceleration, a=dvdt=2×0.5π×0.5πcos(0.5πt+π3)
Maximum acceleration, amax=2×0.5π×0.5π=π22 cms2
and the magnitude of maximum acceleration, |amax|=π22=π22 cms2
Hence, the correct choice is (c).


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