Question

A particle experiences constant acceleration for $6s$ after starting from rest. If it travels a distance $s_1$ in the first $2s$, a distance $s_2$ in the next $2s$ and a distance $s_3$ in the last $2s$, then $s_1:s_2:s_3$ is:

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

Answer 1

The correct option is C $1:3:5$

$s_1=\frac{1}{2}a(2{)}^2=2a$
$s_2=\left(\frac{1}{2}a\right(4{)}^2-\frac{1}{2}a\left(2{)}^2\right)=6a$
$s_3=\left(\frac{1}{2}a\right(6{)}^2-\frac{1}{2}a\left(4{)}^2\right)=10a$

Hence, $s_1:s_2:s_3=2a:6a:10a$
$=1:3:5.$