c-3.The radius vector of a pointArelative to the origin varies with ti

1.	c-3.The radius vector of a pointArelative to the origin varies with time t asrat 1-bt2 j , where a and bare positive constants and i and j are the unit vectors of the x and y axes. Find(i) The equation of the point's trajectory y (x); plot this function(ii) The time dependence of the velocity v and acceleration a vectors as well as of the moduli ofthese quantities
Answer» First break componentsx=at --------(1)y=bt^2---------(2)from equation (1)t=x/aput t value in equation (2)y=b (x/a)^2=bx^2/a^2 hencey=bx^2/a^2=(b/a^2) x^2

c-3.The radius vector of a pointArelative to the origin varies with time t asrat 1-bt2 j , where a and bare positive constants and i and j are the unit vectors of the x and y axes. Find(i) The equation of the point's trajectory y (x); plot this function(ii) The time dependence of the velocity v and acceleration a vectors as well as of the moduli ofthese quantities

Answer»

First break componentsx=at --------(1)y=bt^2---------(2)from equation (1)t=x/aput t value in equation (2)y=b (x/a)^2=bx^2/a^2

hencey=bx^2/a^2=(b/a^2) x^2

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