Question

The two ends of a train moving with uniform acceleration pass a certain point with velocities $6kmph$ and $8kmph$ respectively. What is the velocity with which the middle point of the train passes the same point?

• A. $7kmph$
• B. $5\sqrt{2}kmph$
• C. $2\sqrt{10}kmph$
• D. $7.5kmph$

Answer 1

The correct option is B $5\sqrt{2}kmph$

The rear point which had initially a velocity of $6kmph$ attained a velocity of $8kmph$ after having a displacement of the length of the train's

Using

$v^2–u^2=2as$

$as=\frac{(8^2-6^2)}{2}=14$

The middle point which had initially a velocity of $6kmph$ will acquire a velocity $V$ after moving through a distance equal to half the length of the train $=\left(s/2\right)$

$V^2=u^2+2a\left(s/2\right)$

$\Rightarrow V^2=u^2+as$

$\Rightarrow V^2=6^2+14$

$\Rightarrow V^2=50$

$V=5\sqrt{2}kmph$