The position vector of a particle is given as R = (t² - 4t +6) î + (t²) ĵ. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to

Differentiating R with respect to time, we get V = (2t - 4) î + (2t) ĵ Again differentiating velocity with respect to time, we get A= (2) î + (2) ĵ Since velocity and acceleration vector are perpendicular to each other, their Dot product should be 0AV =  (2t - 4) î + (2t) ĵ .  (2) î + (2) ĵ = 04t - 8 +4t = 08t = 8t =1 s (Answer)