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 t0 at which the velocity
vector forms an angle n/4 with the acceleration vector.
