The driver of a train, moving at a speed v,, sights another
train at a distance d of him moving in the same direction
with a slower speed vz. He applies the brakes and gives
a constant retardation a to his train. Find the condition
that the collision of both trains is avoided.
(1)
dz
V - U₂
a
(2) dz (\-v)?
2a
(3)
dz
V, U₂
2a
(4) dz (v; -v)?
a
cs
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Answer:
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Relative velocity v
12
=v
1
−v
2
,
Relative separation s
12
=d,
Relative acceleration a
12
=a
1
−a
2
=−f
Let at time t , trains collides.
Using s=ut+
2
1
at
2
⇒d=(v
1
−v
2
)t−
2
1
ft
2
⇒ft
2
−2(v
1
−v
2
)t+2d=0,
For real solution of t, (2(v
1
−v
2
))
2
−4×f×2d>0
⇒
2f
(v
1
−v
2
)
2
>d
∴ For collision v
1
>v
2
and
2f
(v
1
−v
2
)
2
>d
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