problem 1.24

 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 moduli 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.