A train covers one half of the distance between two stations with an average speed V1 and remaining half with an average speed V2 . Let V denote the average speed of the train for the whole journey. Show that 1 V = 1 2 [ 1 V1 + 1 V2 ]
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Answer:
Explanation:
If The half distance (x) covered with the speed v
1
in t
1
time.
Using formula of speed, v
1
=
t
1
x
so, t
1
=
v
1
x
And another half distance (x), covered with speed v
2
in time t
2
.
so, v
2
=xt
2
t
2
=
v
2
x
Average Velocity=
Total time
Total distance
Total time=t
1
+t
2
=
v
1
x
+
v
2
x
=
v
1
v
2
(v
2
∗x+v
1
∗x)
Total distance =x+x=2x
On putting the values of total distance and total time in the formula of average speed, we get
Average speed=
(
v
1
∗v
2
v
2
x+v
1
x
)
2x
V=
(v
1
+v
2
)
2v
1
v
2
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