A particle perfroms SHM with a period T and amplitude a. The mean velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is
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a
a/T
b
2a/T
c
3a/T
d
a/2T
answer is C.
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Detailed Solution
x=acosωta/2=acosωt0 or cosπ3=cosωt0 or π3=ωt0 ∴t0=π3ω v=dxdt=−aωsinωt∴ v¯=∫0π/3ω vdt∫0π/3ω dt But ω=2πT ∴ v¯=3aT