Question

The tro ends of a train moving with constant acceleration pass a certain point with velocities $u$ and $3u$. The velocity with which the middle point of the train passes the same point is

• A. $2u$
• B. $\frac{3}{2}u$
• C. $\sqrt{5}u$
• D. $\sqrt{10}u$

Answer 1

The correct option is C $\sqrt{5}u$

The tro ends of a train moving with constant acceleration pass a certain point with velocities $u$ and $3u.$ The velocity with which the middle point of the train passes the same point is

$S=(v^2-u^2)/\left(2a\right)$

If Length of train is L then

$L=\left(\right(3u{)}^2-u^2\left)/\right(2a)$

$L=4u^2/a—-\left(1\right)$

Midpoint is at Distance$L/2$

$S=(v^2-u^2)/\left(2a\right)$

$L/2=(v^2-u^2)/\left(2a\right)$

From equation (1)

$(2u{)}^2/a=(v^2-u^2\left)/\right(2a)$

$4u^2=v^2-u^2$

$v^2=5u^2$

$v=u\surd 5$

Velocity with which middle point passes the same point is $u\surd 5$