A particle moving in the xy-plane has velocity components dx/dt = 6 + 2t and dy/dt = 4 + t where x and y are measured in metres and t in seconds. (i) Integrate the above equation to obtain x and y as functions of time, given that the particle was initially at the origin. (ii) Write the velocity v of the particle in terms of the unit vectors i and j. (iii) Show that the acceleration of the particle may be written as a = 2i + j. (iv) Find the magnitude of the acceleration and its direction with respect to the x-axis.
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