A stone falls freely under gravity. It covers distances $x_{1}, x_{2}$ and $x_{3}$ in the first $t$

Question

A stone falls freely under gravity. It covers distances $x_{1}, x_{2}$ and $x_{3}$ in the first $t$ seconds, the first $2t$ seconds, and the first $3t$ seconds respectively. The relation between $x_{1}, x_{2}$ and $x_{3}$ is

Professor PC Thomas Classes · Answer

(a) : Distance covered by the stone starting from rest is $S = \frac{1}{2}gt^2$. \ Distance in first $t$ seconds, $x_{1}=\frac{1}{2} g(t)^{2}$ \ Distance in first $2t$ seconds, $x_{2}=\frac{1}{2} g(2t)^{2}=4\left(\frac{1}{2} g t^{2}ight)=4x_{1}$ \ Distance in first $3t$ seconds, $x_{3}=\frac{1}{2} g(3t)^{2}=9\left(\frac{1}{2} g t^{2}ight)=9x_{1}$ \ Therefore, the relation is $x_{1}=\frac{x_{2}}{4}=\frac{x_{3}}{9}$.