The velocity of a particle is given by `v=v_(0) sin omegat`, where `v_(0)` is constant and `omega=2pi//T`. Find the average velocity in time interval `t=0 `to `t=T//2.`

The velocity of a particle is given by `v=v_(0) sin omegat`, where `v_

1.	The velocity of a particle is given by `v=v_(0) sin omegat`, where `v_(0)` is constant and `omega=2pi//T`. Find the average velocity in time interval `t=0 `to `t=T//2.`
Answer» `v=v_(0) sin omega t` `barv=(overset(T//2)underset(0)intvdt sin(omegat)dt)/(overset(T//2)underset(0)int dt)` `(v_(0)(\|-cos(omegat)\|_(0)^(T//2))/omega)/(\|t\|_(0)^(T//2)=(T/2-0))` `=(2v_(0))/(omegaT)[{-cos((omegaT)/2)}-{-cos(0)}]` `=(2v_(0))/(2pi)(-cospi+1)` `=v_(0)/pi{-(-1)+1} (cos pi=cos 180^(@)=-1)` `=2/piv_(0)`

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The velocity of a particle is given by `v=v_(0) sin omegat`, where `v_(0)` is constant and `omega=2pi//T`. Find the average velocity in time interval `t=0 `to `t=T//2.`

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