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A particle moves so that its positi...

A particle moves so that its position vector varies with time as `vec(r)=A cos omega t hat(i) +A sin omega t hat(j) `. If ` (dvec(r))/(dt)` gives instantaneous velocity. Find the initial velocity of particle.

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`vec(r)=A cos omega t hat(i)+A sin omega t hat(j)`
`vec(v)=(d vec(r))/(dt) = (Ad(cos omega t ) hat (i))/(dt) +(Ad (sin omega t) hat(j))/(dt)`
`=-A omega sin omega t hat(i) + A omega cos omega t hat(j)`
` "At" t=0`
` v=- A omega sin 0 hat(i) + A omega cos 0 hat(j)=A omega hat(j)`
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