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A point moves in the plane xy according ...

A point moves in the plane `xy` according to the law `x=at`, `y=at(1-alphat)`, where a and `alpha` 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_0` at which the velocity vector forms an angle `pi//4` with the acceleration vector.

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