Consider a body of mass 1.0 kg at rest at the origin at time $t=0$. A force $\vec{F}=(\alpha t \hat{i}+\beta \hat{j})$ is applied on the body, where $\alpha=1.0 \mathrm{Ns}^{-1}$ and $\beta=1.0 \mathrm{~N}$. The torque acting on the body about the origin at time $t=1.0 \mathrm{~s}$ is $\vec{\tau}$. Which of the following statements is (are) true?
Select ALL correct options:
A
$|\vec{\tau}|=\frac{1}{3} N m$
B
The torque $\vec{\tau}$ is in the direction of the unit vector $+\hat{k}$
C
The velocity of the body at $t=1 \mathrm{~s}$ is $\vec{v}=\frac{1}{2}(\hat{i}+2 \hat{j}) \mathrm{ms}^{-1}$
D
The magnitude of displacement of the body at $t=1 \mathrm{~s}$ is $\frac{1}{6} \mathrm{~m}$
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