Question

A train is moving along a straight path with uniform acceleration its engine passes across a pole with a velocity of $60km/h$ and the end (guard'svan) passes across same pole with a velocity of $80km/h$. The middle point of the train will pass across same pole with a velocity

• A. $90km/h$
• B. $70.7m/h$
• C. $65km/h$
• D. $75km/h$

Answer 1

The correct option is B $70.7m/h$

Let S be the length of the train t be the time taken by the full train to cross the pole and a be uniform acceleration of train from -

$\Rightarrow v^2-u^2=2as$

$\Rightarrow \frac{{80}^2-{60}^2}{2a}=s$

$\Rightarrow s=\frac{6400-3600}{2a}$

$=\frac{1400}{2a}⟶\left(1\right)$

The middle part of the train covers half of total distance $\frac{s}{2}=\frac{700}{a}$ from $v^2-u^2=2as,$

$\Rightarrow v^2-{60}^2=2a\times \frac{70}{a}=1400$

$v^2=1400+3600=\sqrt{5000}=70.7km/hr$

Hence, the answer is $70.7km/hr.$