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Physics Part I

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Physics

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Class 10 Class 12
Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km/hr in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

Here,

Velocity of train A, straight u subscript straight A equals 72 km divided by hr equals 20 space straight m divided by straight s 

Velocity of train B, straight u subscript straight B equals 72 km divided by hr equals 20 space straight m divided by straight s
 
Acceleration of train A, straight a subscript straight A equals 0 space straight m divided by straight s comma     

Acceleration of train B, straight a subscript straight B space equals space 1 space straight m divided by straight s squared

Let initially A be ahead of B by a distance d. Let SB and SA be the distances travelled by trains B and A respectively in 50s.

As at t = 50 s the position of both the trains is same.

Therefore, 
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Now,

  straight S subscript straight A equals straight u subscript straight A straight t plus 1 half straight a subscript straight A straight t squared 

  space space space equals 20 cross times 50 plus 1 half cross times 0 cross times left parenthesis 50 right parenthesis squared equals 1000 space straight m

 straight S subscript straight B equals straight u subscript straight B straight t plus 1 half straight a subscript straight B straight t squared

   equals 20 cross times 50 plus 1 half cross times 1 cross times left parenthesis 50 right parenthesis squared equals 2250 space straight m 

∴ original distance between them is, 

space space space space straight d equals straight S subscript straight B minus straight S subscript straight A

     equals space 2250 space minus space 1000 space equals space 1250 space straight m 

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