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The position vector of a aprticle is giv...

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

A

`1 sec`

B

`2 sec`

C

`1.5 sec`

D

not possible

Text Solution

Verified by Experts

The correct Answer is:
A
`(A)`
`vec(r)=(t^(2)-4t+6)hat(i)=t^(2)hat(j),vec(v)=(dvec(r))/(dt)=(2t-4)hat(i)+2that(j), vec(a)=(dvec(v))/(dt)=2hat(i)+2hat(j)`
if `vec(a)` and `vec(v)` are perpendicular
`vec(a).vec(v)=0`
`(2hat(i)+2hat(j)).((2t-4)hat(i)+2that(j))=0`
`8t-8=0`
`t=1sec.`
`Ans. t=1 sec`.
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