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Question: Answered & Verified by Expert
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
MathematicsDifferential EquationsJEE Main
Options:
  • A $\log _{10} e$
  • B $2 \log _e 10$
  • C $2 \log _{10} e$
  • D $\frac{1}{2} \log _{10} e$
Solution:
1086 Upvotes Verified Answer
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 $x=99, t=\log _e 100=2 \log _e 10$

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