Question
The structure of solid crystals is investigated by using
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$\vec{r}(t)=\alpha t^3 \hat{i}+\beta t^2 \hat{j}$
where $\alpha=10 / 3 \mathrm{~m} \mathrm{~s}^{-3}, \beta=5 \mathrm{~m} \mathrm{~s}^{-2}$ and $m=0.1 \mathrm{~kg}$. At $t=1 \mathrm{~s}$, which of the following statement($s$) is(are) true about the particle?
($A$) The velocity $\vec{v}$ is given by $\vec{v}=(10 \hat{i}+10 \hat{j}) \mathrm{ms}^{-1}$
($B$) The angular momentum $\vec{L}$ with respect to the origin is given by $\vec{L}=-15 / 3) \hat{k} \mathrm{~N} \mathrm{~m} \mathrm{~s}$
($C$) The force $\vec{F}$ is given by $\vec{F}=(\hat{i}+2 \hat{j}) \mathrm{N}$
($D$) The torque $\vec{\tau}$ with respect to the origin is given by $\vec{\tau}=-(20 / 3) \hat{k} \mathrm{~N} \mathrm{~m}$