A force `vecF=6t^(2)hati+4thatj` is acting on a particle of mass 3 kg then what will be velocity of particle at t=3 second and if at t=0, particle is at rest:-

Options

A. `18 hati+6hatj`
B. `18hati+12hatj`
C. `12hati+6hatj`
D. none

Answer

A

Explanation

`veca=(vecF)/(m)=(1)/(3)(6t^(2)hati+4hatj)=2t^(2)hati+(4)/(3)thatj`
`(dvecv)/(dt)=2t^(2)hati+(4)/(3)thatjrArrint_(0)^(v)dvecv=int_(0)^(3)(2t^(2)hati+(4)/(3)thatj)dt`
`vecv=[(2t^3))/(3)hati+(4)/(3)(t^(2))/(2)hatj]_(0)^(3)`
`=(2)/(3)(3)^(3)hati+(2)/(3)(3)^(2)hatj=18hati+6hatj`