A charged particle moves under the influence of an electric field. Its x-position andy-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. Letˆiandˆjdenote unit vectors in the eastward and northward direction. a) At arbitrary time t, what is the particle’s velocity? Express your answer as a vectorusingˆi,ˆj notation, and also by specifying the magnitude and direction. b) At arbitrary time t, what is the particle’s acceleration? Again, useˆi,ˆjnotation,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 andy-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. Letˆiandˆjdenote unit vectors in the eastward and northward direction. a) At arbitrary time t, what is the particle’s velocity? Express your answer as a vectorusingˆi,ˆj notation, and also by specifying the magnitude and direction. b) At arbitrary time t, what is the particle’s acceleration? Again, useˆi,ˆjnotation,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 andy-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. Letˆiandˆjdenote unit vectors in the eastward and northward direction.}

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

^{b) At arbitrary time t, what is the particle’s acceleration? Again, useˆi,ˆjnotation,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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