Question

A particle experiences a constant acceleration for $20\text{s}$ starting from rest. If it travels a distance $S_1$ in the first $10\text{s}$ and a distance $S_2$ in the next $10\text{s}$, then:

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

Answer 1

The correct option is B $S_1=\frac{S_2}{3}$

Let the acceleration be $a$.

$S_1=ut+\frac{1}{2}a{t}^2$
Here, $u=0$ and the time interval is $10\text{s}.$
$\Rightarrow S_1=\frac{1}{2}a\times 100$
Or, $S_1=50a....\left(i\right)$

Now, speed of the particle at the end of $10\text{s}$,
$v=u+at$
$\Rightarrow v=10a$

So, for the next $10\text{s}$,
$S_2=ut+\frac{1}{2}a{t}^2$
$\Rightarrow S_2=100a+50a=150a....\left(ii\right)$

From Eq.$\left(i\right)$ and $\left(ii\right)$,
$S_1=\frac{S_2}{3}$