Question

A body starts from rest and is uniformly acclerated for $30s$. The distance travelled in the first $10s$ is $x_1$, next 10 s is $x_2$ and the last 10 s is $x_3$. Then $x_1:x_2:x_3$ is the same as

• A. $1:2:4$
• B. $1:2:5$
• C. $1:3:5$
• D. $1:3:9$

Answer 1

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

Given that u = 0;

We use the equation:

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

Distance traveled between $t_1$ and $t_2$ is:

$s=\frac{1}{2}a(t_2^2-t_1^2)$

For first ten seconds:

$x_1=\frac{1}{2}a\left({10}^2\right)=50a$

For second ten seconds:

$x_2=\frac{1}{2}a({20}^2-{10}^2)=150a$

For third ten seconds:

$x_2=\frac{1}{2}a({30}^2-{20}^2)=250a$

Hence ratio of :

$x_1:x_2:x_3$ is

$50a:150a:250a$

Which is:

$1:3:5$ hence option C is correct.