Question

A train is moving with uniform acceleration .the two ends of the train pass trough a point on the track with velocity v1 and v2 with what velocity the middle point of the train would pass trough the same point

Answer 1

see the attachment for sol################

Answer 2

I have taken v2 as v while v1 as u.
Velocity of mid point = v1

We all know that,
v2-u2=2as or v2=u2+2as -----> (1)
a=v2-u2/2s
Now for the mid-point of the train
s1=s/2
a1=v12-u2/2s1
a1=v12-u2/2s/2
a1=v12-u2/s or v12=u2 + as ----> (2)
from (1) and (2) you will get
as= v2-u2/2
v12=u2 + as
v12= v2+u2 /2
V=under root v2+u2/2.