question 41 - 1wq7ltii

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question 41

Asked by purvi16saini2004 | 16 Jul, 2022, 03:26: PM

Expert Answer

Displacement

begin mathsize 14px style x left parenthesis t right parenthesis space equals space 5 space cos space open parentheses 2 pi t plus pi over 4 close parentheses end style

velocity

begin mathsize 14px style v left parenthesis t right parenthesis space equals fraction numerator d x over denominator d t end fraction space equals space minus 10 pi space sin space open parentheses 2 pi t plus pi over 4 close parentheses end style

Acceleration

begin mathsize 14px style a left parenthesis t right parenthesis space equals fraction numerator d v over denominator d t end fraction space equals space minus 20 pi squared space cos space open parentheses 2 pi t plus pi over 4 close parentheses end style

at t = 1.5 s, Displacement

begin mathsize 14px style x left parenthesis t right parenthesis space equals space 5 space cos space open parentheses 3 pi plus pi over 4 close parentheses space equals space 5 space cos space stretchy left parenthesis fraction numerator 5 pi over denominator 4 end fraction stretchy right parenthesis space equals space minus 3.54 space m end style

at t = 1.5 s , Acceleration

begin mathsize 14px style a left parenthesis t right parenthesis space space equals space minus 20 pi squared space cos space open parentheses 3 pi plus pi over 4 close parentheses space equals space minus 20 space pi squared space cos open parentheses fraction numerator 5 pi over denominator 4 end fraction close parentheses space equals space minus 140 space m divided by s squared end style

Answer :- option (3) displacement = -3.54 m , magnitude of acceleration = 140 m/s²

Answered by Thiyagarajan K | 16 Jul, 2022, 07:47: PM

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