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The position vector of a particle is giv...

The position vector of a particle is given `vecr= 2thati+3t^(2)hatj-5hatk` calculate the velocity and speed of the particle at any instant 't'.

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`vecr = 2thati + 3t^2 hatj - 5hatk`
Velocity `vecv = (dvecr)/(dt) =(d)/(dt) (2t hati + 3t^2 hatj - 5 hatk)`
`vecv = (2hati + 6t hatj) ms^(-1)`
Speed `|vecv| = sqrt((2)^2 + (6)^2) = sqrt(40) = 2sqrt(10) ms^(-1)`
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