A lizard, at an initial distance of 21 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

JEE Main · 2005 · 08 May 2005 · Offline · Chapter_pending

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

Answer: (C)

Measuring from the lizard's starting point, in time

t

the lizard (starting from rest with acceleration

2

) covers

\frac{1}{2} (2) t^{2} = t^{2}

cm, while the insect,

21

cm ahead and moving at

20

cm/s, is at

21 + 20 t

. Catching the insect requires

t^{2} = 21 + 20 t

, that is

t^{2} - 20 t - 21 = 0

, which factors as

(t - 21) (t + 1) = 0

. Taking the positive root, the lizard catches the insect after

21

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option