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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 toA. `1 sec`B. `2 sec`C. `1.5 sec`D. not possible |
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Answer» Correct Answer - 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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