A train accelerates from rest at a constant rate 𝛼 for distance 𝑥1 and time 𝑡1. After that it retards to rest at constant rate 𝛽 for distance 𝑥2 and time 𝑡2. Then it is found that

Question : A train accelerates from rest at a constant rate 𝛼 for distance 𝑥1 and time 𝑡1. After that it retards to rest at constant rate 𝛽 for distance 𝑥2 and time 𝑡2. Then it is found that

(A) \dfrac{x_{1}}{x_{2}}=\dfrac{\alpha }{\beta }=\dfrac{t_{1}}{t_{2}}

(B) \dfrac{x_{1}}{x_{2}}=\dfrac{\beta }{\alpha }=\dfrac{t_{1}}{t_{2}}

(C) \dfrac{x_{1}}{x_{2}}=\dfrac{\beta }{\alpha }=\dfrac{t_{2}}{t_{1}}

(D) (C) \dfrac{x_{1}}{x_{2}}=\dfrac{\beta }{\alpha }=\dfrac{t_{2}}{t_{1}}

Answer : option (C)

Solution :

A train accelerates from rest at a constant rate 𝛼 for distance 𝑥1 and time 𝑡1. After that it retards to rest at constant rate 𝛽 for distance 𝑥2 and time 𝑡2. Then it is found that
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