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notes001 (79) - MATH 2203 Quiz 2 Solutions February 14,...

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MATH 2203 Quiz 2 Solutions February 14, 2011 NAME_______________________________ 1) The position of a particle moving in the xy plane at time t is given by r ( t ) = cos (2 t ) i + 3 sin (2 t ) j . Compute the velocity vector ( v ( t ) ), the speed ( v ( t ) ), the acceleration vector ( a ( t ) x and y whose graph is the path of the particle. Answers: v ( t ) = v ( t ) = a ( t ) = Equation of path of motion: Show your work here: Solution: The velocity is v ( t ) = 2 sin (2 t ) i + 6 cos (2 t ) j and the acceleration is a ( t ) = 4 cos (2 t ) i 12 sin (2 t ) j . The speed is v ( t ) = j v ( t ) j = q 4 sin 2 (2 t ) + 36 cos 2 (2 t ) . x and y ) for the path of motion, note that parametric equations for the path of motion are x = cos (2 t ) y = 3 sin (2 t ) . 1
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We can write these as x = cos (2 t ) y 3 = sin (2 t ) and observe that x 2 + y 3 ± 2 = cos 2 (2 t ) + sin 2 (2 t ) = 1 . Thus the path along which the motion takes place is
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This note was uploaded on 02/05/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

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notes001 (79) - MATH 2203 Quiz 2 Solutions February 14,...

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