A point moves in the plane xy according to the law x = at, y = at

Question:

A point moves in the plane xy according to the law x = at, y = at (1- at), where a and α 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 t0 at which the velocity vector forms an angle π/4 with the acceleration vector.