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+t^{2}

y(t) = 6−4t+ 0.5t^{2}

^{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?}