question_answer

A body starting from rest moves with uniform acceleration. What is the ratio of distances travelled in successive intervals of time?

Answer:

\[S=ut+\frac{1}{2}a{{t}^{2}}\] \[\Rightarrow S\propto {{t}^{2}}(\because a=k,\,\,u=0)\] \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}:\,\,\,.............\,{{S}_{n}}\] \[={{1}^{2}}:{{2}^{2}}:{{3}^{2}}:\,\,\,.............\,\,{{n}^{2}}\] \[=1:4:9\,\,\,.............\,\,{{n}^{2}}\]