A train stopping at 2 stations 4 km apart takes 4 min on the journey from one of the station to the other.Assuming that it first accelerates with uni.acceleration x and then that of uniform retardation y, prove that (1/x)+(1/y)=2

Chilukuri Sai Kartik Grade: 12

        A train stopping at 2 stations 4 km apart takes 4 min on the journey from one of the station to the other.Assuming that it first accelerates with uni.acceleration x and then that of uniform retardation y, prove that (1/x)+(1/y)=2

8 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert

147 Points

										Dear Chilukuri
let t1 is time of acceleration and s1 is distance covered in this time .v is the velocity after time t
let t2 is time of retardation and s2 is distance covered in this time  .
v²=0²-2xs1
s1=v²/2x..............1
v=0+xt1
v/x=t1 ..................2
 
and  0=v-yt2
   t2=v/y .................3
0²=v²-2ys2
s2=v²/2y..............4
add 2 and 3
1/x  +1/y  =(t1+t2)/v
               =4/v..........5
add 1 and 4
s1+s2 =v²/2(1/x +1/y)
4=v²/2(1/x +1/y)
or (1/x +1/y) =8/v²
put value of v from equation 5
1/x +1/y  =2


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