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The velocity of a particle is given by $v = v_{0} \sin ω t$ $v_{0}$ is constant and $ω = 2 π / T .$ Find the average velocity in time interval t = 0 to t = T/2.

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detailed solution

Correct option is D

v=v0sinωtv¯=∫0T/2v0sin(ωt)dt∫0T/2 dt=v0|-cos(ωt)|0T/2ωT2=2v0ωT-cosωT2-{-cos(0)}=2v02π(-cosπ+1)=v0π{-(-1)+1}cosπ=cos180°=-1=2πv0

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The velocity of a particle is given by v=v0sinωt v0 is constant and ω=2π/T. Find the average velocity in time interval t = 0 to t = T/2.

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The velocity of a particle is given by $v = v_{0} \sin ω t$ $v_{0}$ is constant and $ω = 2 π / T .$ Find the average velocity in time interval t = 0 to t = T/2.