Question

A body starts from rest and is uniformly accelerated for $30s$ . The distance travelled in the first $10s$ is $S_1$ , next $10s$ 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
$S_1=v_{0}t+\frac{1}{2}a{t}^2$
$v_1=v_0+at$
$S_2={\text{v}}_1\text{t}+\frac{1}{2}{\text{at}}^2$ $\Rightarrow v_{0}t+\frac{3}{2}a{t}^2$
${\text{v}}_2={\text{v}}_1+\text{at}$
$={\text{v}}_0+2\text{at}$
${\text{S}}_3={\text{v}}_2\text{t}+\frac{1}{2}{\text{at}}^2$
$={\text{v}}_0\text{t}+\frac{5}{2}{\text{at}}^2$
${\text{v}}_0=0$
${\text{S}}_1=\frac{1}{2}{\text{at}}^2$ ; ${\text{S}}_2=\frac{3}{2}{\text{at}}^2$ ; ${\text{S}}_3=\frac{5}{2}{\text{at}}^2$
${\text{S}}_1\text{ : }{\text{S}}_2\text{ : }{\text{S}}_3=\text{1}\text{ : }3\text{ : }5$