The position vector of a particle is given as `vec(r)=(t^(2)-4t+6)hat(i)+(t^(2))hat(j)`. 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)hat(i)+t_(2) hat(j)`,
`vec(v)=(d vec(r))/(dt)=(2t-4)hat (i)+ 2t hat(j)`
`vec(a)=(d vec(v))/(dt)=2 hat(i)+2 hat(j)`
If `vec(a)` and `vec(v)` are perpendicular
`vec(a). vec(v) =0`
`(2 hat(i)+2 hat(j)).((2t-4)hat(j)+2t hat(j))=0`
`8t-8 =0`
`t=1sec`.