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A particle moves in a straight line with a velocity given by $\frac{d x}{d t}=x+1$ ( $x$ is the distance described). The time taken by a particle to traverse a distance of 99 meter is
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The correct answer is:
$2 \log _e 10$
$\frac{d x}{d t}=x+1 \Rightarrow \log (x+1)=t+c$
Putting $t=0, x=0$, we get ${ }^{\log 1-c} \Rightarrow c=0$
$\therefore t=\log (x+1) . \quad$ For $x=99, t=\log _e 100=2 \log _e 10$
Putting $t=0, x=0$, we get ${ }^{\log 1-c} \Rightarrow c=0$
$\therefore t=\log (x+1) . \quad$ For $x=99, t=\log _e 100=2 \log _e 10$
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