question_answer

A body is falling under gravity. What is the ratio of distance covered in 1st, 2nd and 3rd seconds of its motion?

Answer:

\[u=0\] \[a=g=9.8\,\,m{{s}^{-2}}\] \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}=?\] \[{{S}_{n}}\propto (2n-1)\,\,(\because u=0\]and g is constant) \[{{S}_{n}}=u+\frac{a}{2}(2n-1)\] \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}=(2\times 1-1):\,\,(2\times 2-1)\]                                                 \[:(2\times 3-1)=1:3:5\] \[\therefore \,\,{{S}_{1}}:{{S}_{2}}:{{S}_{3}}=1:3:5\]