Q124 / 180 · KCET 2014 · Physics
A body starts from rest and moves with constant acceleration for \( t \) s. It travels a distance \( x_{1} \) in
first half of time and \( x_{2} \) in next half of time, then
first half of time and \( x_{2} \) in next half of time, then
- A\( x_{2}=x_{1} \)
- B\( x_{2}=2 x_{1} \)
- Correct answerC\( x_{2}=3 x_{1} \)
- D\( x_{2}=4 x_{1} \)
Solution
Initial velocity $=0$ and acceleration is constant.
Distance travelled in first half of time $=\chi_{1}$
Distance travelled in next half of time $=x_{2}$
Therefore, acceleration $=\frac{x_{2}-x_{1}}{t^{2}} \rightarrow$ (1)
Now, $x_{1}=\frac{1}{2}$ at $^{2}$ because initial velocity is zero. Substitute in Eq. (1), we get
$$
\begin{array}{l}
a=\frac{x_{2}-\frac{1}{2} a t^{2}}{t^{2}} \\
\Rightarrow a t^{2}=x_{2}-\frac{1}{2} a t^{2} \\
\Rightarrow x_{2}=a t^{2}+\frac{1}{2} a t^{2} \\
\Rightarrow x_{2}=3 \times \frac{1}{2} a t^{2}
\end{array}
$$
Thus $x_{2}=3 x_{1}$
Hence, the correct answer is option: 'C'.