Consider a body of mass 1.0 𝑘𝑔 at rest at the origin at time 𝑡 = 0. A force $$\overrightarrow{F}=(\alpha t \hat{i}+\beta \hat{j})$$ is applied on the body, where $$\alpha=1.0 N S^{-1}$$ and $$ \beta=1.0$$N The torque acting on the body about the origin at time 𝑡 = 1.0 𝑠 is 𝜏⃗. Which of the following statements is (are) true?

A

$$\mid\overrightarrow{\tau} \mid= \frac{1}{3}$$ Nm

B

The torque $$\overrightarrow{\tau}$$ is in the direction of the unit vector $$+ \hat{K}$$

C

The velocity of the body at $$t = 1 s$$ is $$\overrightarrow{V} = \frac{1}{2}(\hat{i} + 2\hat{j})ms^{-1}$$

D

The magnitude of displacement of the body at $$t = 1 s$$ is $$\frac{1}{6}$$ m