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vijay kumar pandey Grade: 12
        

if a variable accleration of -(1/2x^2) is working then at what time the particle will reach at x =0.25 m.if the velocity is 0 at x=1m at t=0.pls give me the analysed solution.

6 years ago

Answers : (1)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
										

Dear Vijay,


Ans:- v dv/dx= -(1/2x^2)


integrating within the limits x=1 to x=x && v=0 to v=v we get,


v²=(1/x - 1)


or v=√(1/x - 1)


Again v= - dx/dt ( negatine sign comes, as with the increase of time x decreases) 


hence   - √x/√(1 - x) dx=dt


 Then integrating from x=1 to .25 and t=0 to t we get


t=∏/3 + √3/4 sec (ans)


 


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Regards,


Askiitians Experts


SOUMYAJIT IIT_KHARAGPUR

6 years ago
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