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:

Question

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: (A) √( v 2+ u 2/2) (B) ( v - u /2) (C) ( u + v /2) (D) √( v 2- u 2/2)

Tardigrade Admin · Accepted Answer

( v prime)2= u 2+2 ad v 2=( v prime)2+2 ad solving, we get v prime=√(v2+u2/2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/d99e53b707cb9645e938994107f84063-.png" />

Q. 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:

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

$\frac{v - u}{2}$

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

$\frac{v ^{2} - u ^{2}}{2}$

$(v^{'})^{2} = u^{2} + 2 a d$
$v^{2} = (v^{'})^{2} + 2 a d$
solving, we get
$v^{'} = \frac{v ^{2} + u ^{2}}{2}$

Q. 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:

2v2+u2​​

2v−u​

2u+v​

2v2−u2​​