Consider a body of mass \( 1.0 \mathrm{~kg} \) at rest at the origin at
\( \mathrm{P} \) time \( t=0 \). A force \( \vec{F}=(\alpha t \hat{i}+\beta \hat{j}) \) is applied on the body,
W 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?
(1) \( |\vec{\tau}|=\frac{1}{3} \mathrm{Nm} \)
(2) The torque \( \vec{\tau} \) is in the direction of the unit vector \( +\hat{k} \)
(3) The velocity of the body at \( t=1 \mathrm{~s} \) is \( \vec{v}=\frac{1}{2}(\hat{i}+2 \hat{j}) \mathrm{ms}^{-1} \)
(4) The magnitude of displacement of the body at \( t=1 \mathrm{~s} \) is \( \frac{1}{6} \mathrm{~m} \)
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