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Both the equations are correct and they will yield the same answer when solved for a question.
you are absolutely right about the differences and i must tell you that when
y vs x graph is given we generally use the 1st equation i.e.
... however there is no boundation that you have to use that one only .. its just that it makes your calculations easy
and
when y vs t graph is given then we use the second equation for the same reason.
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