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

• Correct answer
  A

  $\left|\overrightarrow{\tau }\right|=\frac{1}{3} Nm$
• B

  The torque $\overrightarrow{\tau }$ is in the direction of the unit vector $+\overrightarrow{k}$
• Correct answer
  C

  The velocity of the body at $t=1 s is \overrightarrow{v}=\frac{1}{2}\left(\widehat{i}+2\widehat{j}\right) m s^{-1}$
• D

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

Hence, the correct answer is options: 'A', 'C'.