An object is moving in the xy-plane and its position after t seconds is r(t)=(t^2 +2t)i+(t+4)j. Find an equation in x and y whose graph is the path of the object.

Matilda Fox

Matilda Fox

Answered question

2022-07-24

An object is moving in the xy-plane and its position after t seconds is r ( t ) = ( t 2 + 2 t ) i + ( t + 4 ) j
Find an equation in x and y whose graph is the path of the object.

Answer & Explanation

ri1men4dp

ri1men4dp

Beginner2022-07-25Added 14 answers

So, we have that in x and y it moves:
x = t 2 + 2 t.....(1)
y = t + 4 t = y 4....(2)
Replacing (2) in (1), we get:
x = ( y 4 ) 2 + 2 ( y 4 ) = y 2 8 y + 16 + 2 y 8 = y 2 6 y + 8

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