Question

the driver of a train travelling at 115km/h sees on the same track 100m in front of him. A slow train travelling in the same direction at 25km/h . The least retardation must be applied to faster train to avoid a collision ?

Answer 1

The least retardation that must be applied to faster train to avoid a collision will be $3.125\frac { m }{ { s }^{ 2 } }$ .

Given:  

Velocity of the driver of a train A travelling  $= 115\frac { km }{ hr }$

Distance = 100m in front of him

Velocity of slow train B $= 25\frac { km }{ hr }$

Velocity of train 'B' with respect to train 'A' $= (115-25) \frac { km }{ hr }$

$VBA = -90\frac { km }{ hr } = -25\frac { m }{ s }$

Since ; ${ v }^{ 2 }\quad ={ \quad u }^{ 2 }-2as$

Since v = 0

Therefore ;

 ${ u }^{ 2\quad }=\quad 2as$

Plug the values ;  

${ (25) }^{ 2 }\quad =\quad 2\times a\times 100 \\\Rightarrow 625\quad =\quad 2\times a\times 100$

Hence;  $a\quad =\quad 3.125\frac { m }{ { sec }^{ 2 } }$

Answer 2

Answer:

Explanation

The least retardation that must be applied to faster train to avoid a collision will be  .

Given:  

Velocity of the driver of a train A travelling  

Distance = 100m in front of him

Velocity of slow train B

Velocity of train 'B' with respect to train 'A'

Since ;

Since v = 0

Therefore ;

 

Plug the values ;  

Hence;  

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