A train stopping at two stations 4 km apart takes 4 minutes on the journey from one station
to the other. Assuming that it first accelerates with uniform acceleration x and then that of
uniform retardation y prove that
1/x + 1/y = 2
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11th
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Motion in a Straight Line
Problems on Equation of Motion
A train stopping at two sta...
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Asked on December 20, 2019 by
Nikita Panwar
A train stopping at two stations 4 km apart takes 4 min on the journey from one of the station to the other. Assuming that it first accelerates with a uniform acceleration x and then that of uniform retardation y, prove that
x
1
+
y
1
=2.
HARD
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ANSWER
Given : u=v=0
Total distance covered S=4km
Total time taken t=4 min
∴ t
1
+t
2
=t ⟹t
2
=t−t
1
........(a)
For 1st part :
V
1
=u+a
1
t
1
=0+xt
1
⟹V
1
=xt
1
.........(1)
Also V
1
2
−0
2
=2(x)S
1
⟹S
1
=
2x
V
1
2
..............(2)
For 2nd part :
0=V
1
+(−y)t
2
∴0=V
1
−y(t−t
1
) ⟹V
1
=y(t−t
1
) .........(3)
Also 0−V
1
2
=2(−y)S
2
⟹ S
2
=
2y
V
1
2
..............(4)
Equating (1) & (2) we get xt
1
=y(t−t
1
) ⟹t
1
=
x+y
yt
⟹ V
1
=xt
1
=
x+y
xyt
Adding (2) & (4), we get S=S
1
+S
2
=
2(xy)
V
1
2
(x+y)
⟹ S=
2(x+y)
xyt
2
Now putting the values, 4=
2(x+y)
(xy)4
2
∴
xy
x+y
=2 ⟹
x
1
+
y
1
=2
solution