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CBSE Class 11-science Answered

A particle moves in XY plane with velocity given by v = (8t-2)i + 2j where t in sec gives v in m/s . If it passes through the point (14m,4m) at t=2 sec , then the equation of path of particle will be ? 
Asked by arunavamitra50 | 02 Jul, 2018, 06:38: PM
answered-by-expert Expert Answer
begin mathsize 12px style v left parenthesis t right parenthesis space equals space fraction numerator d r over denominator d t end fraction space equals space fraction numerator d x over denominator d t end fraction i with rightwards arrow on top space plus space fraction numerator d y over denominator d t end fraction j with rightwards arrow on top space equals space left parenthesis 8 t minus 2 right parenthesis i with rightwards arrow on top space plus space 2 j with rightwards arrow on top

fraction numerator d x over denominator d t end fraction space equals space open parentheses 8 t space minus space 2 close parentheses space semicolon space space x left parenthesis t right parenthesis space equals space integral open parentheses 8 t space minus space 2 close parentheses d t space equals space 4 t squared space minus space 2 t space plus C
w h e n space t space equals space 2 comma space x space equals space 14 space m comma space h e n c e space C space equals space 2 space semicolon space space space x left parenthesis t right parenthesis space equals space 4 t squared minus 2 t space plus space 2 space equals space 2 left parenthesis 2 t squared minus t plus 1 right parenthesis

fraction numerator d y over denominator d t end fraction equals space 2 semicolon space y left parenthesis t right parenthesis space equals space integral 2 d t space equals space 2 t plus C
w h e n space t equals 2 comma space y space equals space 4 space m comma space h e n c e space C space equals 0 space a n d space y left parenthesis t right parenthesis space equals space 2 t

e q u a t i o n space o f space p a t h comma space r left parenthesis t right parenthesis space equals space 2 left parenthesis 2 t squared minus t plus 1 right parenthesis space i with rightwards arrow on top space plus space 2 t space j with rightwards arrow on top end style
Answered by Thiyagarajan K | 03 Jul, 2018, 03:45: PM
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