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An object starts from rest at the point $P=(2,3,1)$ and moves with an acceleration of:

$${\bf a}(t)=t^2{\bf i} +3{\bf j}+t{\bf k}$$

...where $||{\bf a}(t)||$ is measured in meter per second per second. Where will the object be after $12$ seconds?

$1730{\bf i}+ 219{\bf j} + 289{\bf k}$

$144{\bf i}+ 3{\bf j} + 12{\bf k}$

$146{\bf i}+ 6{\bf j} + 13{\bf k}$

$576{\bf i}+ 36{\bf j} + 72{\bf k}$

$578{\bf i}+ 39{\bf j} + 73{\bf k}$