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a train stopping at two stations 4 KM apart takes 4 min of the journey from one station to another.assuming that it first accelerate with a uniform acceleration x and that of uniform retardation y.prove that 1/x+1/y=2

a train stopping at two stations 4 KM apart takes 4 min of the journey from one station to another.assuming that it first accelerate with a uniform acceleration x and that of uniform retardation y.prove that 1/x+1/y=2


 

Grade:12

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
8 years ago

Dear student,

Let us assume, it takes a minutes to cover a distance of z metres. In this time, it accelerates with uniform acceleration x.

So, it would take 4-a minutes to cover the distance of 4-z metres. In this time, it decelerates with uniform deceleration y.

Hence, the acceleration produced for the first part would be equal to:

x=(2z/a^2)

The final velocity achieved would be equal to:

v_f=xa

Now for the decelartion part, we get:

(xa)^2=2y(4-a)

This yields:

y=2/(4-a)

Hence, solving the equation fo x, we get:

x=2/a.

Thus, solving these two together, yields the required result.

Thanks & Regards
Sumit Majumdar, 
askIITians Faculty
Ph.D, IIT Delhi

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