A point moves in the plane xy according to the law x = at,
y = at (1. — at), where a and a are positive constants, and t is
time. Find:
(a) the equation of the point's trajectory y (x); plot this function;
(b) the velocity v and the acceleration w of the point as functions
of time;
(c) the moment t, at which the velocity vector forms an angle It/4
with the acceleration vector_