Question

A goods train accelerating uniformly on a straight railway
track, approaches an electric pole standing on the side of
track. Its engine passes the pole with velocity u and the
guard's room passes with velocity v. The middle wagon of
the train passes the pole with a velocity
U + v
2
(6)
11
+ V
(a)
2​

Answer 1

Given: Engine passes the pole with velocity u and the guard's room passes with velocity v.

To find: The middle wagon of  the train passes the pole with which velocity?

Solution:

• We have given the velocity of engine while passing through pole as u and through guards room as v.

• So now let s be the distance between two ends.

• Let a be the constant acceleration while moving.

• We know the formula for distance as :

             2as = v² - u²

             as = v² - u² / 2     ..................(i)

• Now let V be the velocity at the mid point. the distance will become s/2.

• Then:  V² - u² = 2a(s/2)

             V² - u² = as   ...................(ii)

• Putting (i) in (ii), we get:

             V² - u² = v² - u² / 2

             V² = v²/2 - u²/2  + u²

             V² = v²/2 + u²/2

             V = √(v²/2 + u²/2)

Answer:

         The middle wagon of  the train passes the pole with √(v²/2 + u²/2) velocity.