Question

A body starts from rest and is uniformly accelerated for $30 \, s$ . The distance travelled in the first $10 \, s$ is $S_{1}$ , next $10 \, s$ is $S_{2}$ and the last 10 s is $S_{3}$ . Then $S_{1}:S_{2 \, }:S_{3}$ is the same as

• A. $1:2:4$
• B. $1:2:5$
• C. $1:3:5$
• D. $1:3:9$

Answer 1

Answer: (C)

a = constant
$S_{1}=v_{0}t+\frac{1}{2}at^{2}$
$v_{1}=v_{0}+at$
$S_{2}=\textit{v}_{1}\textit{t}+\frac{1}{2}\textit{at}^{2}$ $\Rightarrow v_{0}t+\frac{3}{2}at^{2}$
$\textit{v}_{2}=\textit{v}_{1}+\textit{at}$
$=\textit{v}_{0}+2\textit{at}$
$\textit{S}_{3}=\textit{v}_{2}\textit{t}+\frac{1}{2}\textit{at}^{2}$
$=\textit{v}_{0}\textit{t}+\frac{5}{2}\textit{at}^{2}$
$\textit{v}_{0}=0$
$\textit{S}_{1}=\frac{1}{2}\textit{at}^{2}$ ; $\textit{S}_{2}=\frac{3}{2}\textit{at}^{2}$ ; $\textit{S}_{3}=\frac{5}{2}\textit{at}^{2}$
$\textit{S}_{1}\text{ : }\textit{S}_{2}\text{ : }\textit{S}_{3}=\text{1}\text{ : }3\text{ : }5$