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  • The motion of a body is given by the equation   where <img alt="v" src

The motion of a body is given by the equation  \frac{dv}{dt}=6-3v where v is the speed in m{{s}^{-1}} and t is the time in second. The body is at rest at t=0. The speed varies with time as

Option: 1

v=(1-{{e}^{-3t}})


Option: 2

v=2(1-{{e}^{-3t}}).


Option: 3

v=(1+{{e}^{-2t}})


Option: 4

v=2(1+{{e}^{-2t}})


Answers (1)

best_answer

\frac{dv}{dt}=6-3v

dt=\frac{dv}{6-3v}

Integrating both sides, we get t=-\frac{1}{3}\ln (6-3v)+C

Where C is the constant of integration

At t=0,v=0

\therefore C=\frac{1}{3}\ln 6

\therefore t=-\frac{1}{3}\ln (\frac{6-3v}{6})

{{e}^{-3t}}=1-\frac{1}{2}v

v=2(1-{{e}^{-3t}})

Posted by

avinash.dongre

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