Question

A body travels for $15\text{sec}$ starting from rest with constant acceleration. If it travels distances $S_1,S_2$ and $S_3$ in the first five seconds, second five seconds and next five seconds respectively the relation between $S_1,S_2$ and $S_3$ is

• A. $S_1=S_2=S_3$
• B. $5S_1=3S_2=S_3$
• C. $S_1=\frac{1}{3}{S}_2=\frac{1}{5}{S}_3$
• D. $S_1=\frac{1}{5}{S}_2=\frac{1}{3}{S}_3$

Answer 1

The correct option is C $S_1=\frac{1}{3}{S}_2=\frac{1}{5}{S}_3$

As per the question the condition of the particle can be represented as

So, using equation of motion we have
$S_1=u{t}_1+\frac{1}{2}a{t}_1^2$
$S_1=\frac{a}{2}[5{]}^2$
$S_1=\frac{a}{2}\left[25\right]$ ... (1)
$S_1+S_2=\frac{a}{2}[10{]}^2\Rightarrow \frac{a}{2}[100]$ ... (2)
from equation $\left(2\right)–$ equation $\left(1\right)$
$S_1+S_2-S_1=\frac{a}{2}[100-25]$
$S_2=\frac{a}{2}\left[75\right]$ ... (3)
$S_1+S_2+S_3=\frac{1}{2}a[15{]}^2$
$100\left(\frac{a}{2}\right)+S_3=\frac{a}{2}\left[225\right]$
$S_3=125\left(\frac{a}{2}\right)$ ... (4)
From equation $\left(1\right),\left(3\right),\left(4\right)$ we have
$S_1:S_2:S_3=25:75:125$
$\Rightarrow S_1:S_2:S_3=1:3:5$