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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

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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