Let's unclick the path R (keeping curve C showing) and put in the origin
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Expression 15: "O" equals left parenthesis, 0 , 0 , 0 , right parenthesisO=0,0,0
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The "position" POINT P when t=(pi)/2, which is the head/end-point of the path (vector) when t = (pi)/2 ... think of this POINT P as the POINT on the curve when t = (pi)/2
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Expression 17: "P" equals left parenthesis, cos StartFraction, pi Over 2 , EndFraction , sin StartFraction, pi Over 2 , EndFraction , StartFraction, pi Over 2 , EndFraction , right parenthesisP=cosπ2,sinπ2,π2
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Next let's think about the velocity vector when t = (pi)/2 .
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The POINT that is the head/end of the velocity VECTOR when t = (pi)/2
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Expression 20: "V" equals left parenthesis, negative 1 , 0 , 1 , right parenthesisV=−1,0,1
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Let's graph the VECTOR for the origin O to the point V
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Expression 22: vector left parenthesis, "O" , "V" , right parenthesisvectorO,V
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and "move" the vector OV as so it's initial/start point is P (rather than the origin O).
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Expression 24: vector left parenthesis, "P" , "P" plus "V" , right parenthesisvectorP,P+V
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Unclick the gray V and vector(O,V).
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Question: If the Grinch turns off the magnetic switch to the magnetized track when time t=(pi)/2, then in what direction will the puffo go?