Question

A body starts from rest and is uniformly accelerated. for $30$ s. The distance travelled in the first $10$s 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

$\begin{array}{c}{x}_1=\frac{1}{2}a{t}^2\\ x_2+x_1=\frac{1}{2}a{\left(2t\right)}^2=4x_1\\ =x_2=3x_1\\ x_1+x_2+x_3=\frac{1}{2}a{\left(3t\right)}^2=9x_1\\ x_3=9x_1-x_1-3x_1=5x_1\\ \therefore 1:3:5\end{array}$

Hence,

option $\left(C\right)$ is correct answer.