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a particle in 1D motion is subjected to an acceleration a = -alpha . t, where alpha is a positive constant. initial velocity is u at t = 0. the velocity of particle after time t is​

Asked by saijayanthno1 8th July 2021, 5:38 PM
Answered by Expert
Acceleration , a = begin mathsize 14px style fraction numerator d v over denominator d t end fraction end style = - α t ......................(1)
where v is velocity function of time 
By integrating eqn.(1) , we get
begin mathsize 14px style integral subscript u superscript v d v space equals space minus alpha integral subscript 0 superscript t d t space end style
where u is initial velocity at t = 0 and v is velocity after time t
we get from above integration , begin mathsize 14px style v space equals space u space minus space 1 half alpha space t squared end style
Answered by Expert 8th July 2021, 5:49 PM
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