The position vector of a particle is given as r^ = (t^2-4t+6)i^ + (t^2)j^ What is the time - Science - Motion

Question

The position vector of a particle is given as r^> = (t^2-4t+6)i^
+ (t^2)j^ What is the time after which the velocity vector and
acceleration vector becomes perpendicular to each other?

Neha Gupta · Accepted Answer

r→=t2-4t+6i⏜ + t2j⏜velocity = drdt= 2t-4i⏜ + 2tj⏜acceleration = dvdt=2i⏜ + 2j⏜a→
v→ = 2t-4i⏜ + 2tj⏜
2i⏜ + 2j⏜when they are pependicular then a
v = 02t-4i⏜ + 2tj⏜
2i⏜ + 2j⏜ = 02t-4×2 + 4t =04t -8+4t = 0t= 1s

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