Question

The position vector is given as r=(t^2-4t+6)i+(t^2)j.the time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to

Answer 1

Diffrerntiate position vector to obtain velocity and again differentiate velocity to obtain acceleration.

Now you have eqn. For velocity and acceleration.
Use a.v = 0
Where a. V is dot product of acceleration and velocity