oblem: 4.3
The two ends of a train moving with uniform
acceleration pass a certain point with
velocity u and v. Find the velocity with
which the middle point of the train passes
the same point
VI
u
Answers
Explanation:
ANSWER
Given:
The length of the train is l.
The velocity of the first end at the point is u.
The final velocity of the other end at the point is v.
The train is moving under uniform acceleration. SO, the relation between the velocities and the distancecovered is given by:
v
2
−u
2
=2al ...........(i)
where l= length of the train
Let the speed of the middle point of the train be v
m
.
To obtain the velocity of the middle point of the train at the point:
and v
m
2
−u
2
=2a⋅
2
1
v
m
2
−u
2
=al .........(ii)
From eqs (i) and (ii)
v
2
−u
2
=2[v
m
2
−u
2
]
v
m
2
=
2
v
2
+u
2
∴v
m
=
(
2
v
2
+u
2
)
.