Below are the motions of the Chicken and the Worm.
The Worm has parametric equations x=3t, y=-t+8, 0≤t≤4.
The Chicken has parametric equations x=t+7, y=t2+1, 0≤t≤4.
The animation is from t=0 to t=4 seconds. You can watch the timeline below the graph. Although their paths intersect, they do not collide. When are the Chicken and the Worm at the point of intersection of their paths? The animation will repeat.

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Plot_2d