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At time $t=0$ the position of the particle is $3 ft$, and at time $t=2$ the position of the particle is $11ft$. At time $t=0$ the velocity of the particle must have been zero. So if its the motion of the particle that has been plotted, then why doesn't it start at the point $(0,3)$? The line also extends backward. What does that mean?
We might think of the moving particle as an ant crawling...Suppose we we want to study how far an ant moves over the course of a couple minutes, say staring at $10$:$00$, it may very well be that the ant has been crawling since $9:58$, but that we don't start measuring distance or time until $10$:$00$.
In this case, we would put $t = 0$ minutes at $10$:$00$. Then given the fact that the ant started moving $2$ minutes earlier, we might say that at $t = -2$, the ant started moving.
In short, we can think of $t = 0$ as representing a relative starting time, relative to when measurement starts, for example.