Multiple choice

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

  1. $20$ s
  2. $1$ s
  3. $21$ s
  4. $24$ s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let t be time. Distance covered by lizard = 0.5 * a * t^2 = 0.5 * 2 * t^2 = t^2. Distance covered by insect = 20t. The lizard catches the insect when t^2 = 21 + 20t. Solving t^2 - 20t - 21 = 0 gives (t - 21)(t + 1) = 0. Since t > 0, t = 21 seconds.

AI explanation

To catch the insect, the lizard must cover the initial 21 cm gap plus the distance the insect crawls in that time. Using the equations of motion, the lizard's distance is s = ut + 1/2 at^2 and since it starts from rest, its distance is 1/2 * 2 * t^2, which is t^2 cm. Setting the lizard's distance equal to the insect's distance plus 21 cm, we get the quadratic equation t^2 = 20t + 21. Solving t^2 - 20t - 21 = 0 gives t = 21 seconds.

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