A particle moves in a straight line with velocity given by $\frac{dy}{dx} = x+ 1$ (x being the distance described). The time taken by the particle to describe 99 metres is :
Answer & explanation
Correct answer: option 2
$\frac{d x}{d t}=x+1 \Rightarrow \frac{d x}{x+1}=d t$
⇒ log(x + 1) = t + c ....(1)
Initially, when t = 0, x = 0
∴ c = 0
∴ log (x + 1) = t
When x = 99, then t = loge (100) = 2 loge 10
Hence (2) is the correct answer.