A radius vector of a point A relative to the origin varies with time t as `r=ati-bt^2j`, where a and
Channel: Doubtnut
Date: 2020-08-23

A radius vector of a point A relative to the origin varies with time t as `r=ati-bt^2j`, where a and b are positive constants, and I and j are the unit vectors of the x and y axes. Find: (a) the equation of the point's trajectory `y(x)`, plot this function,  (b) the time dependence of the velocity v and acceleration w vectors, as well as of the moduli of these quantities,  (c) the time dependence of the angle `alpha` between the vectors w and v,  (d) the mean velocity vector averaged over the first t seconds of motion, and the modulus of this vector.