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Asked by anam.asfia99 3rd November 2018, 11:26 AM
Answered by Expert
Answer:
Equation governing the motion of body :-  dv/dt  = (1-2v) , where v is velocity at time t.
 
The given equation can be written as begin mathsize 12px style fraction numerator d v over denominator 1 minus 2 v end fraction space equals space d t space space space space space space o r space space space space space space space open parentheses negative 1 half close parentheses open parentheses fraction numerator negative 2 d v over denominator 1 minus 2 v end fraction close parentheses space equals space d t space space space space space space space space o r space space space space space space space space space space space fraction numerator begin display style negative 2 d v end style over denominator begin display style 1 minus 2 v end style end fraction space equals space minus 2 d t space................. left parenthesis 1 right parenthesis end style
By integerating eqn.(1) on both sides, we get
begin mathsize 12px style ln left parenthesis 1 minus 2 v right parenthesis space equals space minus 2 t space space space space space o r space space space space space space space 1 minus 2 v space space equals space e to the power of negative 2 t end exponent space space space space space space o r space space space space space space v space equals space 1 half open parentheses 1 minus e to the power of negative 2 t end exponent close parentheses end style
Answered by Expert 3rd November 2018, 8:53 PM
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