JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Kinematics

An engine of a train, moving with uniform acceleration, passes the signal - post with velocity

u

and the last compartment with velocity

v

. The velocity with which middle point of the train passes the signal post is :

Answer: (B)

Solution

Let the train have length

L

and uniform acceleration

a

. Between the engine reaching the post and the last compartment reaching it, the train advances through its own length:

v^{2} = u^{2} + 2 a L \Rightarrow 2 a L = v^{2} - u^{2}

The middle point reaches the post when the train has advanced

\frac{L}{2}

from the first instant, so its speed

v_{m}

there satisfies

v_{m}^{2} = u^{2} + 2 a (\frac{L}{2}) = u^{2} + \frac{v ^{2} - u ^{2}}{2} = \frac{u ^{2} + v ^{2}}{2}

The middle point therefore passes the signal post with speed

\frac{v ^{2} + u ^{2}}{2}

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option