A radius vector of a point A relative to the origin varies with time t as r = ati - bt2j, where a and b are positive constants, and i and j are the unit vectors of the x and y axes. Find:
(a) The equation of the point's trajectory y (x); plot this function;
(b) The time dependence of the velocity v and acceleration w vectors, as well as of the modulus of these quantities;
(c) The time dependence of the angle a between the vectors w and v;
(d) The mean velocity vector averaged over the first t seconds of motion, and the modulus of this vector.