The magnitude of velocity and acceleration and velocity of a particle moving in a plane, whose position vector `r = 3t^(2)hati+2thatj+hatk` at t = 2s are respectively
Note In the question paper sequence is given, (acceleration and velocity) which is not matching with any of option given.

Options

A. `sqrt(148), 6`
B. `sqrt(144), 6`
C. `sqrt(13),3`
D. `sqrt(14),3`

Answer

A

Explanation

Given, `r=3t^(2)hati+2t hatj+hatk`
(i) Velocity vector, `v=(dr)/(dt)=6t hati+2hatj`
Magnitude of velocity vector,
`|v|_(t=2)=sqrt((12)^(2)+(2)^(2))=sqrt(148)`
(ii) Acceleration vector, `a=(dv)/(dt)=6hati`
Magnitude of acceleration `|a|_(t=2)=sqrt((6^(2)))=6`