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The position vector for a particle is re...

The position vector for a particle is represented be `vecr=3t^(2)hati+5thatj+6hatk`, find the velocity and speed of the particle at t=3 sec.

Text Solution

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`vecv=(bar(dr))/(dt)=6thati+5hatj`
The velocity at any time .t. is given by `vecv=6thati+5hatj`. The magnitude of velocity is speed. The speed at any time .t. is then given by
speed `=sqrt((6t)^(2)+5^(2))=sqrt(36t^(2)+25)`
Now the velocity at t=3 sec is given by
`vecv=6(3)hati+5hatj=18hati+5hatj`
and speed at t=3 sec, is given by
speed `sqrt(349)m//s`.
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