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A radius vector of a point A relative to...

A radius vector of a point A relative to the origin varies with time t as `r=ati-bt^2j`, 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 moduli of these quantities,
(c) the time dependence of the angle `alpha` 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.

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