A point moves in the plane `xy` according to the law `x=at`, `y=at(1-alphat)`, where a and `alpha`
Channel: Doubtnut
Date: 2020-08-23

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.