A charged particle moves under the influence of an electric field. Its x-position and y-position, as a function of time, are observed to be x(t) = 4 + 3t + t2 y(t) = 6− 4t + 0.5t2 meters, where the x- and y-direction are east and north, respectively. Letˆi andˆj denote unit vectors in the eastward and northward direction. a) At t = 2, what is the particle’s velocity? Express your answer as a vector usingˆi,ˆj notation, and also by specifying the magnitude and direction. b) At t = 2, what is the particle’s acceleration? Again, useˆi,ˆj notation,and also specify the magnitude and direction. c) How fast is the particle moving at the moment it is moving due east?

A charged particle moves under the influence of an electric field. Its x-position and y-position, as a function of time, are observed to be x(t) = 4 + 3t + t2 y(t) = 6− 4t + 0.5t2 meters, where the x- and y-direction are east and north, respectively. Letˆi andˆj denote unit vectors in the eastward and northward direction. a) At t = 2, what is the particle’s velocity? Express your answer as a vector usingˆi,ˆj notation, and also by specifying the magnitude and direction. b) At t = 2, what is the particle’s acceleration? Again, useˆi,ˆj notation,and also specify the magnitude and direction. c) How fast is the particle moving at the moment it is moving due east?

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Question

A charged particle moves under the influence of an electric field. Its x-position and y-position, as a function of time, are observed to be

x(t) = 4 + 3t + t²

y(t) = 6− 4t + 0.5t²

^{meters, where the x- and y-direction are east and north, respectively. Letˆi andˆj denote unit vectors in the eastward and northward direction.}

^{a) At t = 2, what is the particle’s velocity? Express your answer as a vector usingˆi,ˆj notation, and also by specifying the magnitude and direction.}

^{b) At t = 2, what is the particle’s acceleration? Again, useˆi,ˆj notation,and also specify the magnitude and direction.}

^{c) How fast is the particle moving at the moment it is moving due east?}

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