Question

A train starts from rest and acquires a speed $v$ with a uniformed acceleration $\alpha$. It then comes to a stop with a uniform deceleration $\beta$. What is the average velocity of the train?

• A. $\frac{\alpha \beta }{\alpha +\beta }$
• B. $\frac{\alpha +\beta }{\alpha \beta }$
• C. $\frac{v}{2}$
• D. $v$

Answer 1

Answer: (C)

$\frac{v}{2}$

From A to B
$S_1=\frac{v^2}{2\alpha }$ $t_1=\frac{v}{\alpha }$
From B to C
$S_2=\frac{v^2}{2\beta }$ $t_2=\frac{v}{\beta }$
avg. velocity $=\frac{S_1+S_2}{t_1+t_2}$

$=\frac{(\frac{v^2}{2\alpha }+\frac{v^2}{2\beta })}{\frac{v}{\alpha }+\frac{v}{\beta }}=\frac{v}{2}$