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  • A particle starts from rest and moves in a st. line with velocity given by dx/dt=(x+1) where x is the distance transversed in time t seconds the time taken by the particle to traverse a distance of 999 metres is

A particle starts from rest and moves in a st. line with velocity given by dx/dt=(x+1) where x is the distance transversed in time t seconds the time taken by the particle to traverse a distance of 999 metres is

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Solution:   

               fracdx(x+1)=dt

         Integrating , we get

         t+c=log_e(x+1)

     For   t=0,x=0Rightarrow c=0     ........(1)

     herefore (1)  becomes

     t=log_e(x+1)       .........(2)

   For    x=999

        t=log_1000=3log_e10.

 

Posted by

Deependra Verma

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