Question

A train accelerates from rest at a constant rate $\alpha$ for distance $X_1$ and time $t_1$. After that it retards to rest at constant rate $\beta$ for distance $X_2$ and time $t_2$. Then, it is found that

• A. $\frac{X_1}{X_2} = \frac{\alpha}{\beta} = \frac{t_1}{t_2}$
• B. $\frac{X_1}{X_2} = \frac{\alpha}{\beta} = \frac{t_2}{t_1}$
• C. $\frac{X_1}{X_2} = \frac{\beta}{\alpha} = \frac{t_1}{t_2}$
• D. $\frac{X_1}{X_2} = \frac{\beta}{\alpha} = \frac{t_2}{t_1}$

Hint:

In uniformly accelerated motion, the relationship between acceleration, distance, and time remains proportional.

Answer 1

The Correct Option is C

For a uniformly accelerated motion, the relationship between acceleration, time, and distance is given by: \[ X = \frac{1}{2} a t^2 \] Thus, the ratio of the distances traveled during acceleration and retardation can be expressed as: \[ \frac{X_1}{X_2} = \frac{\beta}{\alpha} = \frac{t_1}{t_2} \]