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Statement of a problem № 24

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A radius vector of a point A relative to the origin varies with time t as r = ati - bt2j, 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 α 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.

Solution:
A radius vector of a point A relative to the origin varies with time t as r = at

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