A train accelerates from rest at a constant r | vedclass

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Question

(b)

$x_1=\frac{1}{2} \alpha t_1^2........(i)$

$x_2=\frac{1}{2} \beta t_2^2........(ii)$

Further, $\quad v_{\max }=\alpha t_1........(iii)$

Vedclass · Accepted Answer

$\frac{x_1}{x_2}=\frac{\beta}{\alpha}=\frac{t_1}{t_2}$

Vedclass · Answer

(b)

$x_1=\frac{1}{2} \alpha t_1^2........(i)$

$x_2=\frac{1}{2} \beta t_2^2........(ii)$

Further, $\quad v_{\max }=\alpha t_1........(iii)$

and $\quad 0=v_{	ext {max }}-\beta t_2........(iv)$

From Eqs.$(iii)$ and $(iv)$, we have

$\frac{\alpha}{\beta}=\frac{t^2}{t_1}$

Then, from Eqs.$(i)$ and $(ii)$,

$\frac{x_1}{x_2}=\frac{t_1}{t_2}=\frac{\beta}{\alpha}$

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 $t_2$. Which of the following relations is correct?

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