Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

A particle moves in the \( xy \)-plane under the action of a constant force \( \vec{F} = 4\hat{i}\text{ N} \). At time \( t \), its position vector is \( \vec{r}(t) = (2t^2\hat{i} + 3t\hat{j})\text{ m} \). The torque \( \vec{\tau} \) of this force about the origin at \( t = 2\text{ s} \) is:

1. A
   \( 24\hat{k}\text{ N}\cdot\text{m} \)
2. B
   \( -24\hat{k}\text{ N}\cdot\text{m} \)
3. C
   \( -12\hat{k}\text{ N}\cdot\text{m} \)
4. D
   \( 16\hat{k}\text{ N}\cdot\text{m} \)