The position vector of a aprticle is given as `vecr=(t^2-4t+6)hati+(t^2)hatj`. The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to

Options

A. 1 sec
B. 2 sec
C. 1.5 sec
D. not possible

Answer

A

Explanation

`vec(r)=(t^2-4t+6)hati+t^2hatj`,`vecv=(dvecr)/(dt)=2hati+2hatj`
If velocity vector and acceleration vector are perpedicular
`veca.vecv=0`
`(2hati+2hatj).((2t-4)hati+2thatj)=0`
`8t-8=0`,`t=1` sec