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If a=g-kv then what is the velocity of the particle for very long time and initially particle is at rest fir time t=0? Where a is acceleration g, k is constant and v is velocity.

Asked by namitapandey08062000 | 11 Oct, 2019, 01:26: PM

Expert Answer

acceleration = a = dv/dt = ( g - kv )

begin mathsize 14px style fraction numerator d v over denominator d t end fraction space equals space g space minus space k space v fraction numerator d v over denominator g space minus space k v end fraction space equals space d t space space space space o r space space space fraction numerator negative k space d v over denominator g minus k v end fraction space equals space minus k space d t B y space i n t e g r a t i n g space b o t h space s i d e s space integral subscript 0 superscript v fraction numerator negative k space d v apostrophe over denominator g minus k v apostrophe end fraction space equals space minus k space integral subscript 0 superscript t d t ln open parentheses fraction numerator g space minus space k space v over denominator g end fraction close parentheses space equals space minus k space t ln open parentheses 1 minus fraction numerator k space v over denominator g end fraction close parentheses space equals space minus space k space t 1 minus space fraction numerator k space v over denominator g end fraction space equals space e to the power of negative k space t end exponent v space equals space g over k open parentheses 1 space minus space e to the power of negative k space t end exponent close parentheses space space............ left parenthesis 1 right parenthesis end style

From eqn.(1), we see that, at t = 0, velocity v = 0

after long time, t →∞ , velocity v = g/k

Answered by Thiyagarajan K | 11 Oct, 2019, 03:00: PM

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