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Describing motion of a particle qualitatively
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[QUOTE="kuruman, post: 6828160, member: 192687"] Yes, I am. Just look at the velocity vector, ##\mathbf{v}=6t^2~\mathbf{\hat i}+2t~\mathbf{\hat j}.## In order for the particle to move parallel to the x-axis, the y-component of the velocity must decrease and approach zero as time increases. Actually, the y-component increases linearly with increasing time, so it will never go to zero. Of course, the x-component increases faster than the y-component which means, as the solution says, that the particle will turn to move closer to being parallel to the x-axis. However, it will never be parallel to the x-axis, even after infinite time has elapsed. [/QUOTE]
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Describing motion of a particle qualitatively
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