Question

A particle experiences a constant acceleration for $20sec$ after starting from rest. if it travels a distance $s_1$ in the first $10sec$ and a distance $s_2$ in the next $10sec$, then

• A. $S_1$ = $\frac{S_2}{3}$
• B. ${\text{S}}_1$ = ${\text{S}}_2$
• C. $S_1$ = $\frac{S_2}{2}$
• D. $S_1$ = $\frac{S_2}{4}$

Answer 1

The correct option is A

$S_1$ = $\frac{S_2}{3}$

Formula Used: $S=ut+\frac{1}{2}a{t}^2$

Given, particle starts from rest, so initial

velocity of the particle will be zero i.e.

$u=0$

Now from second equation of motion

As
$S=ut+\frac{1}{2}a{t}^2$

$S_1=\frac{1}{2}a(10{)}^2=50a\dots (i)$

As
$v=u+at$
Velocity acquired by particle in $10sec$.

$V=a\times 10$

For next $10sec$,

$S_2=\left(10a\right)\times 10+\frac{1}{2}\left(a\right)\times (10{)}^2$

$S_2=150a\dots \left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$

$S_1=\frac{S_2}{3}$