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.

The position vector for a particle is represented be vecr=3t^(2)hati+5

1.	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.
Answer» Solution :`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`.