Question

A body travels for $15\text{sec}$ starting from rest with constant acceleration. If it travels $S_1,S_2$ and $S_3$ in the first 5 seconds, second 5 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 $S_1=\frac{1}{3}{S}_2=\frac{1}{5}{S}_3$

Since the body starts from rest. Therefore $u=0$.
By using second equation of motion
Distance covered in first 5 seconds will be
$S_1=\frac{1}{2}a(5{)}^2=\frac{25a}{2}$ ------(1)
Distance covered in first 10 seconds will be
$S_1+S_2=\frac{1}{2}a(10{)}^2=\frac{100a}{2}$
$\Rightarrow S_2=\frac{100a}{2}-S_1=75\frac{a}{2}$ ---------(2) Distance covered in first 15 seconds will be
$S_1+S_2+S_3=\frac{1}{2}a(15{)}^2=\frac{225a}{2}$
$\Rightarrow S_3=\frac{225a}{2}-S_2-S_1=\frac{125a}{2}$---------(3)
On comparing (1), (2) and (3) we will get
$S_1=\frac{1}{3}{S}_2$ and $S_1=\frac{1}{5}{S}_3$