A lizard, at an initial distance of $21 \mathrm{~cm}$ behind an insect, moves from rest with an acceleration…

A lizard, at an initial distance of $21 \mathrm{~cm}$ behind an insect, moves from rest with an acceleration of $2 \mathrm{~cm} / \mathrm{s}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20 \mathrm{~cm} / \mathrm{s}$. Then the lizard will catch the insect after
  1. $20 \mathrm{~s}$
  2. $1 \mathrm{~s}$
  3. $21 \mathrm{~s}$
  4. $24 \mathrm{~s}$

Solution

$ \begin{aligned} & \frac{1}{2} 2 t^2=21+20 t \\ & \Rightarrow t=21 . \end{aligned} $

Asked in: JEE Main 2005

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